PDC drill bit using optimized side rake angle

ABSTRACT

A fixed cutter drill bit and a method for designing a fixed cutter drill bit includes simulating the fixed cutter drill bit drilling in an earth formation. A performance characteristic of the simulated fixed cutter drill bit is determined. A side rake angle distribution of the cutters is adjusted at least along a cone region of a blade of the fixed cutter drill bit to change the performance characteristic of the fixed cutter drill bit.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 11/329,976, filed on Jan. 11, 2006, which is a continuation inpart of U.S. patent application Ser. No. 11/041,895, filed on Jan. 24,2005, both of which are herein incorporated by reference in theirentirety.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to fixed cutter drill bits used to drillboreholes in subterranean formations. More specifically, the inventionrelates to methods for modeling the drilling performance of a fixedcutter bit drilling through an earth formation, methods for designingfixed cutter drill bits, methods for improving and/or optimizing thedrilling performance of a fixed cutter drill bit, and to drill bitsformed using such methods.

2. Background Art

Fixed cutter bits, such as polycrystalline diamond compact (PDC) drillbits, are commonly used in the oil and gas industry to drill well bores.One example of a conventional drilling system for drilling boreholes insubsurface earth formations 100 is shown in FIG. 1. This drilling systemincludes a drilling rig 101 used to turn a drill string 103 whichextends downward into a well bore 105. Connected to the end of the drillstring 103 is a fixed cutter drill bit 109.

As shown in FIG. 2, a fixed cutter drill bit 111 typically includes abit body 113 having an externally threaded connection at one end 115,and a plurality of blades 117 extending from the other end of bit body113 and forming the cutting surface of the bit 113. A plurality ofcutters 119 are attached to each of the blades 117 and extend from theblades to cut through earth formations when the bit 111 is rotatedduring drilling. The cutters 119 deform the earth formation by scrapingand shearing. The cutters 119 may be tungsten carbide inserts,polycrystalline diamond compacts, milled steel teeth, or any othercutting elements of materials hard and strong enough to deform or cutthrough the formation. Hardfacing (not shown) may also be applied to thecutters 119 and other portions of the bit 111 to reduce wear on the bit111 and to increase the life of the bit 111.

Significant expense is involved in the design and manufacture of drillbits and in the drilling of well bores. Having accurate models forpredicting and analyzing drilling characteristics of bits can greatlyreduce the cost associated with manufacturing drill bits and designingdrilling operations because these models can be used to more accuratelypredict the performance of bits prior to their manufacture and/or usefor a particular drilling application. For these reasons, models havebeen developed and employed for the analysis and design of fixed cutterdrill bits.

Two of the most widely used methods for modeling the performance offixed cutter bits or designing fixed cutter drill bits are disclosed inSandia Report No. SAN86-1745 by David A. Glowka, printed September 1987and titled “Development of a Method for Predicting the Performance andWear of PDC drill Bits” and U.S. Pat. No. 4,815,342 to Bret et al. andtitled “Method for Modeling and Building Drill Bits,” and U.S. Pat. Nos.5,010,789, 5,042,596, and 5,131,478, which are all incorporated hereinby reference. While these models have been useful in that they provide ameans for analyzing the forces acting on the bit, their accuracy as areflection of drilling might be improved because these models rely ongeneralized theoretical approximations (typically some equations) ofcutter and formation interaction. A good representation of the actualinteractions between a particular drill bit and the particular formationto be drilled is useful for accurate modeling. The accuracy andapplicability of assumptions made for all drill bits, all cutters, andall earth formations can affect the accuracy of the prediction of theresponse of an actual drill bit drilling in an earth formation.

In one popular model for drill bit design, it is assumed that thecenterline of the drill bit remains aligned with the centerline of thebore hole in which the drill bit is drilling. This type of centerlineconstrained model might be referred to as a “static model,” even thoughthe model calculates incremental dynamic rotation. The term static asapplied to this type of modeling means not varying centerline alignment.In such prior modeling and fixed cutter drill bit design, there waslittle focus on the use of side rake angles of the cutters to improveperformance of the drill bit. The focus was on the rate of penetrationobtained and thus the cutter layout, position, and back rake angle werethe parameters of predominate interest to improve cutting performance.

Fixed cutter drill bits are desired that have side rake angles anddistributions of side rake angles that provide improved performance andstability. A method is desired for modeling the overall cutting actionand drilling performance of a fixed cutter bit that takes intoconsideration and uses side rake angles and/or side rake angledistribution of cutters along blades of fixed cutter drill bits toimprove and to optimize drill bit performance not only for rate ofpenetration but also for dynamic stability so that a desirable rate ofpenetration can be maintained during drilling.

BRIEF SUMMARY OF THE INVENTION

The invention relates to methods for modeling the performance of fixedcutter bit drilling earth formations. The invention also relates tomethods for designing fixed cutter drill bits and methods for optimizingdrilling parameters for the drilling performance of a fixed cutter bit.In one embodiment, the invention relates to modifying a side rake angledistribution for cutters on the drill bit to improve and/or to optimizeperformance of a fixed cutter drill bit that is modeled.

According to one aspect of one or more embodiments of the presentinvention, a method for modeling the dynamic performance of a fixedcutter PDC drill bit with the design optimized using a dynamiccenterline analysis to provide a fixed cutter drill bit with improvedperformance including improved stability during drilling in earthformations. It has been discovered by the inventors using a dynamiccenterline analysis and model, that modifications of the side rake angleof cutters and particularly the distribution of side rake angles alongselected regions of the drill bit can improve the stability of the drillbit during drilling.

In other aspects of the invention, the modeling method can includesselecting a drill bit as a starting model to be simulated, selecting anearth formation to be represented as drilled, and simulating the bitdrilling the earth formation. The simulation according to these aspectsof the invention includes numerically rotating the bit, calculating bitinteraction with the earth formation during the rotating, anddetermining the resultant imbalance forces and predicting the stabilityof the drill bit.

In other aspects, the invention also provides a method for dynamicallymodeling a drill bit during simulated drilling in an earth formation.“Dynamically modeling” as used in this disclosure means modeling a drillstring without an assumed constraint that the centerline of the drillbit is aligned with the centerline of the hole bored into the earthformation. Thus, if the drill bit wobbles or gyrates at the end of adrill string during drilling, the dynamic model accounts for theincreased depth of cut for certain cutters and the decreased depth ofcut for other cutters. The centerline of the drill bit for dynamicallymodeling a drill bit is not arbitrarily constrained to align with thecenterline of the bore hole. For improved accuracy, the centerline ofthe drill bit is constrained by appropriately modeled physical anddynamic features of the drill string components, including the number ofcomponents, as size, length, strength, modulus of elasticity of eachcomponent and of the connectors between components, contact of thecomponents with the bore hole, impact forces, friction forces, and/orother features that may be associated with a given drill stringconfiguration. Empirical data for a drill bit and/or for a given earthformation can also be used to modify calculation coefficients tofacilitate the accuracy of the calculations.

It has been discovered by the inventors that performance of a drill bitdesign can be predicted in some instances by modeling a drill bitdrilling in an earth formation based upon a constrained centerlineanalysis. In cases where less than optimum performance is predicted, theperformance can be improved by modifying the side rake angles and/or theside rake angle distribution.

In other aspects, the invention also provides a method for modeling aselected drill bit in a selected earth formation using static modeling(defined as modeling assuming that the centerline of the drill bit isaligned with the centerline of the hole bored into the earth formation)for purposes of determining wear predictions for the cutters of thedrill bit, modifying the drill bit model according to the static wearmodel and dynamically modeling the drill bit with the static wear modelcharacteristics substituted into the dynamic model calculations.

It has been discovered by the inventors that stability and performanceof a drill bit design can be predicted by dynamically modeling acenterline trajectory of the drill bit during drilling. For one exampleonly, a small diameter trajectory pattern is an indication of drill bitstability while drilling. Other trajectory patterns can also provideindications of drill bit stability in particular situations. It has beendiscovered by the inventors that in cases where instability ispredicted, the stability can be improved by modifying the side rakeangle distribution of cutters to adjust the centerline trajectorypattern to one that has a smaller diameter variation or that otherwiseindicates drilling stability.

It has further been discovered that stability of a drill bit can bepredicted using a dynamic centerline model to calculate a Beta anglebetween radial and circumferential vector components of imbalancedforces acting at the center of the face of the drill bit duringdrilling. Modifications to the design are made, and particularly,according to one embodiment of the invention, modifications to the siderake angle distribution are made, to decrease the magnitude of the totalresultant imbalance forces and to increase the proportion of drillingtime that the Beta angle is at or near β=180°.

It has further been discovered that the predicted bottom hole drillingpattern can be smoothed, the diameter of the trajectory of thecenterline can be reduced or minimized, and/or the portion of the timethat a dynamically modeled Beta angle is at or near to 180 degrees canby increased, and thus the stability of the drill bit drilling in anearth formation can be improved and/or optimized by modifying the siderake angle distribution of cutters along regions of the drill bit.

It has further been found useful to modify the distribution of side rakeangles of cutters along the cone region of the drill bit.

It has further been found useful to modify the side rake angledistribution of cutters along the nose region of the drill bit.

According to one alternative embodiment of the invention, a methodincludes generating a visual representation of one or more of the bottomhole pattern, the total imbalance forces on the drill bit, the side rakeinduced imbalance forces on the drill bit, the centerline trajectory,and the Beta angle between radial and circumferential components oftotal imbalance forces for a fixed cutter drill bit dynamically drillingin an earth formation and designing a fixed cutter drill bit bymodifying the side rake angle of cutters positioned along a portion ofthe drill bit.

In another aspect, the invention provides a method for optimizing siderake angle distribution for cutters of a fixed cutter drill bit basedupon a representation of the drill bit showing the bottom hole pattern,the total imbalance forces on the drill bit, the side rake inducedimbalance forces on the drill bit, the centerline trajectory, and/or theBeta angle (β) for the drill bit during dynamically simulated drillingrotation in an earth formation and modifying the drill bit design tosmooth the predicted bottom hole pattern, to reduce the total imbalanceforces on the drill bit, to reduce the side rake induced imbalanceforces on the drill bit, to improve the centerline trajectory, and/or toincrease the percentage of time during dynamic drilling that the Betaangle is at or near to β=180°, so that the stability of the drill bitdesign is improved or optimized.

In other aspects, the invention also provides a method for modeling aselected drill bit in a selected earth formation, simulating the drillbit drilling in an earth formation, determining the stability of thedrill bit by determining a bottom hole pattern, determining the totalimbalance forces on the drill bit, determining the side rake inducedimbalance forces on the drill bit, determining the centerlinetrajectory, and/or determining the Beta angle between the radial and thecircumferential components of imbalance forces over a selected period ofthe simulated drilling, displaying a graphical depiction of the bottomhole pattern, the total imbalance forces on the drill bit, the side rakeinduced imbalance forces on the drill bit, the centerline trajectory,and/or the Beta angle over a period of time during drilling, modifyingthe side rake angle distribution of cutters along a portion of the drillbit to improve predicted stability by improving the bottom hole pattern,the total imbalance forces on the drill bit, the side rake inducedimbalance forces on the drill bit, the trajectory, and or the Beta angleand repeating the simulating, determining, displaying, and modifying atleast until the predicted performance of the drill bit is improvedand/or optimized.

In other aspects, the invention also provides a fixed cutter drill bitdesigned by the method of the invention.

Other aspects and advantages of the invention will be apparent from thefollowing description and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic diagram of a conventional drilling system fordrilling earth formations.

FIG. 2 shows a perspective view of a prior art fixed-cutter bit.

FIG. 3 shows a flow chart of a method for determining the dynamicresponse of a drilling tool assembly drilling through an earthformation.

FIG. 4 shows a flow chart of one embodiment of the method predicting thedynamic response of a drilling tool assembly drilling through an earthformation in accordance with the method shown in FIG. 3.

FIGS. 5A-C show a flowchart of a method for modeling the performance ofa fixed cutter drill bit drilling in an earth formation.

FIG. 6 shows a flow chart of a method for determining an optimal valueof at least a side rake angle distribution as drilling tool assemblydesign parameter.

FIG. 7 shows a flow chart of one embodiment of the method fordetermining an optimal value of at least a side rake angle distributionas a design parameter in accordance with the method shown in FIG. 6.

FIG. 8 schematically shows a cutter element in relation to a drill bitacting against a formation.

FIGS. 9A-C shows nomenclature for a drill bit cutter in relation to aformation for purposes of modeling the cutter.

FIG. 10A-E shows a drill bit cutter in relation to a formation forpurposes of modeling the cutter.

FIG. 11 shows a partial end view of a fixed cutter bit with a typicaldistribution of side rake angles along one exemplary blade and in whichthe side rake angle distribution is not optimum.

FIG. 12 shows a partial end view of a fixed cutter bit with a modifieddistribution of side rake angles along one exemplary blade and in whichthe modified side rake angle distribution improves performance over theside rake angle distribution shown in FIG. 11.

FIG. 13 shows a schematic layout of fixed cutters on an end view of adrill bit and showing the cone region of the bit and an adjacent noseregion.

FIG. 14 shows a schematic layout of the cut profile generated across oneradial plane by the rotation of the fixed cutters on the drill bit ofFIG. 13.

FIG. 15 shows a partial schematic end view layout of cutters on oneblade having a modified side rake angle distribution applied to cuttersin the cone region of the drill bit.

FIG. 16 shows one example of graphically displaying and modeling dynamicresponse of a fixed cutter drill bit drilling through different layersand through a transition between the different layers, in accordancewith an embodiment of the present invention.

FIG. 17 shows a graphical display of a group of worn cuttersillustrating different extents of wear on the cutters in accordance withan embodiment of the invention.

FIG. 18 shows an example of modeling and of graphically displayingperformance of individual cutters of a fixed cutter drill bit, forexample cut area shape and distribution, together with performancecharacteristics of the drill bit, for example imbalance force vectors,and Beta angle between the components in accordance with an embodimentof the present invention.

FIG. 19 shows a historic graphical plot of a side rake imbalance forcessimulated according to a typical side rake angle distribution that isnot optimum.

FIG. 20 shows a historic graphical plot of a side rake imbalance forcessimulated according to an improved side rake angle distributionaccording to one embodiment of the invention.

FIG. 21 shows a bottom hole cutting pattern simulated according to atypical side rake angle distribution that is not optimum.

FIG. 22 shows a bottom hole cutting pattern simulated according to animproved side rake angle distribution according to one embodiment of theinvention.

FIG. 23 shows a centerline trajectory pattern simulated according to atypical side rake angle distribution that is not optimum.

FIG. 24 shows a centerline trajectory pattern simulated according to animproved side rake angle distribution according to one embodiment of theinvention.

FIG. 25 shows a historic graphical plot of total imbalance forcessimulated according to a typical side rake angle distribution that isnot optimum.

FIG. 26 shows a historic graphical plot of a total imbalance forcessimulated according to an improved side rake angle distributionaccording to one embodiment of the invention.

FIG. 27 shows a historic graphical plot of a Beta angle between thecircumferential and the radial components of the total imbalance forcessimulated according to a typical side rake angle distribution that isnot optimum.

FIG. 28 shows a historic graphical plot of a Beta angle between thecircumferential and the radial components of the total imbalance forcessimulated according to an improved side rake angle distributionaccording to one embodiment of the invention.

FIG. 29 shows a flow diagram of an example of a method for optimizing adrill bit design by simulating, graphically displaying, adjusting,designing, and making a fixed cutter drill bit in accordance with anembodiment of the present invention.

FIG. 30 shows a partial end view of a fixed cutter bit with analternative modification of the distribution of side rake angles alongone exemplary blade having cutters in the cone region that are normal toa vertical plane through the centerline of the bit and moving the cutterfaces forward of the normal plane to modify the side rake angledistribution and thereby improve performance according to one embodimentof the invention.

FIG. 31 shows a schematic end view layout of fixed cutters both onleading blades and on trailing blades of a drill bit and showingalternative side rake angle distributions on the leading blades anddifferent distributions on the trailing blades

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention provides methods for predicting a performanceresponse of a drilling tool assembly drilling an earth formation,methods for optimizing a drilling tool assembly design, methods foroptimizing drilling operation parameters, and methods for optimizingdrilling tool assembly performance.

The present invention provides methods for modeling the performance of afixed cutter drill bit drilling in an earth formation. In one aspect, amethod takes into account actual interactions between cutters and earthformation during drilling. Methods in accordance with one or moreembodiments of the invention may be used to design a fixed cutter drillbit, to optimize the performance of the drill bit, to optimize thedynamic response of the drill bit in connection with an entire drillstring during drilling, or to generate visual displays representingperformance characteristics of the drill bit drilling in an earthformation. In one particular embodiment, the invention usefully providesa representation of radial and circumferential imbalance forcecomponents and a Beta (β) angle between such components during simulateddrilling.

In accordance with one aspect of the present invention, one or moreembodiments of a method for modeling the dynamic performance of a fixedcutter drill bit drilling in an earth formation includes selecting adrill bit design and an earth formation to be represented as drilled,wherein a geometric model of the drill bit, a geometric model of a drillstring on which the drill bit is to be supported for drilling, and ageometric model of the earth formation to be represented as drilled aregenerated. The method also includes incrementally rotating the drillstring with the drill bit to simulate drilling in the formation andcalculating the interaction between the cutters on the drill bit and theearth formation during the incremental rotation. The method furtherincludes determining the forces on the cutters of the drill bit duringthe incremental rotation, determining the interaction between the drillbit and the earth formation, and determining resultant radial andcircumferential components of imbalance forces acting on the drill bitand the Beta angle between such imbalance force components during aperiod of full or partial rotation of the drill bit in the formation. Bygraphically displaying at least a representation of the Beta angle for adrill bit during drilling, a design of a drill bit can be obtained thatprovides useful performance characteristics.

Methods for determining the dynamic response of a drilling tool assemblyto drilling interaction with an earth formation were initially disclosedin U.S. Pat. No. 6,785,641 by Huang, which is assigned to the assigneeof the present invention and incorporated herein by reference in itsentirety. New methods developed for modeling fixed cutter drill bits aredisclosed in U.S. Patent Application No. 60/485,642 by Huang, filed onJul. 9, 2003, titled “Method for Modeling, Designing, and OptimizingFixed Cutter Bits,” assigned to the assignee of the present applicationand incorporated herein by reference in its entirety. Methods disclosedin the '642 application may advantageously allow for a more accurateprediction of the actual performance of a fixed cutter bit in drillingselected formations by incorporating the use of actual cuttingelement/earth formation interact data or related empirical formulas toaccurately predict the interaction between cutting elements and earthformations during drilling. Embodiments of the invention disclosedherein relate to the use of methods disclosed in the '641 patentcombined with methods disclosed in the '642 application and other novelmethods related to drilling tool assembly design.

FIG. 1 shows one example of a drilling tool assembly that may bedesigned, modeled, or optimized in accordance with one or moreembodiments of the invention. The drilling tool assembly includes adrill string 103 coupled to a bottom hole assembly (BHA) 107. The drillstring 103 includes one or more joints of drill pipe. A drill string mayfurther include additional components, such as tool joints, a kelly,kelly cocks, a kelly saver sub, blowout preventers, safety valves, andother components known in the art. The BHA 107 includes at least a drillbit. A BHA 107 may also include one or more drill collars, stabilizers,a downhole motor, MWD tools, LWD tools, jars, accelerators, push the bitdirectional drilling tools, pull the bit directional drilling tools,point stab tools, shock absorbers, bent subs, pup joints, reamers,valves, and other components.

While in practice, a BHA comprises a drill bit, in embodiments of theinvention described below, the parameters of the drill bit, required formodeling interaction between the drill bit and the bottomhole surface,are generally considered separately from the BHA parameters. Thisseparate consideration of the drill bit allows for interchangeable useof any drill bit model as determined by the system designer.

To simulate the dynamic response of a drilling toot assembly, such asthe one shown in FIG. 1, components of the drilling tool assembly needto be defined. For example, the drill string may be defined in terms ofgeometric and material parameters, such as the total length, the totalweight, inside diameter (ID), outside diameter (OD), and materialproperties of each of the various components that make up the drillstring. Material properties of the drill string components may includethe strength and elasticity of the component material. Each component ofthe drill string may be individually defined or various parts may bedefined in the aggregate. For example, a drill string comprising aplurality of substantially identical joints of drill pipe may be definedby the number of drill pipe joints of the drill string, and the ID, OD,length, and material properties for one drill pipe joint. Similarly, theBHA may be defined in terms of geometrical and material parameters ofeach component of the BHA, such as the ID, OD, length, location, andmaterial properties of each component.

The geometry and material properties of the drill bit also need to bedefined as required for the method selected for simulating drill bitinteraction with earth formation at the bottom surface of the wellbore.Examples of methods for modeling drill bits are known in the art, seefor example U.S. Pat. No. 6,516,293 to Huang, U.S. Pat. No. 6,213,225 toChen for roller cone bits, and U.S. Pat. No. 4,815,342; U.S. Pat. No.5,010,789; U.S. Pat. No. 5,042,596; and U.S. Pat. No. 5,131,479, each toBrett et al. for fixed cutter bits, which are each hereby incorporatedby reference in their entireties. Other methods for modeling, designing,and optimizing fixed cutter drill bits are also disclosed in U.S. PatentApplication No. 60/485,642, previously incorporated herein by reference.

To simulate the dynamic response of a drilling tool assembly drillingthrough an earth formation, the wellbore trajectory in which thedrilling tool assembly is to be confined should also be defined alongwith its initial bottomhole geometry. The wellbore trajectory may bestraight, curved, or a combination of straight and curved sections atvarious angular orientations. The wellbore trajectory may be defined interms of parameters for each of a number of segments of the trajectory.For example, a wellbore defined as comprising N segments may be definedby the length, diameter, inclination angle, and azimuth direction ofeach segment along with an index number indicating the order of thesegments. The material or material properties of the formation definingthe wellbore surfaces can also be defined.

Additionally, drilling operation parameters, such as the speed at whichthe drilling tool assembly is rotated and the rate of penetration or theweight on bit (which may be determined from the weight of the drillingtool assembly suspended at the hook) may also be defined. Once thedrilling system parameters are defined, they can be used along withselected interaction models to simulate the dynamic response of thedrilling tool assembly drilling an earth formation as discussed below.

In connection with dynamically modeling a drill bit, it has been foundthat the dynamic model can often benefit from input obtained from staticmodeling.

Method for Simulating

In one aspect, the invention provides a method for determining thedynamic response of a drilling tool assembly during a drillingoperation. Advantageously, in one or more embodiments, the method takesinto account interactions between an entire drilling tool assembly andthe drilling environment. The interactions may include the interactionbetween the drill bit at the end of the drilling tool assembly and theformation at the bottom of the wellbore. The interactions between thedrilling tool assembly and the drilling environment may also include theinteractions between the drilling tool assembly and the side (or wall)of the wellbore. Further, interactions between the drilling toolassembly and drilling environment may include the viscous dampingeffects of the drilling fluid on the dynamic behavior of the drillingtool assembly. In addition, the drilling fluid also provides buoyancy tothe various components in the drilling tool assembly, reducing theeffective masses of these components.

A flow chart for one embodiment of a method in accordance with an aspectof the present invention is shown in FIG. 3. The method includesinputting data characterizing a drilling operation to be simulated 102.The input data may include drilling tool assembly parameters, drillingenvironment parameters, and drilling operation parameters. The methodalso includes constructing a mechanics analysis model for the drillingtool assembly 104. The mechanics analysis model can be constructed usingfinite element analysis with drilling tool assembly parameters andNewton's law of motion. The method further includes determining aninitial static state of the drilling tool assembly in the drillingenvironment 106 using the mechanics analysis model along with drillingenvironment parameters. Then, based on the initial static state andoperational parameters provided as input, the dynamic response of thedrilling tool assembly in the drilling environment is incrementallycalculated 108.

Results obtained from calculation of the dynamic response of thedrilling tool assembly are then provided as output data. The output datamay be input into a graphics generator and used to graphically generatevisual representations characterizing aspects of the performance of thedrilling tool assembly in drilling the earth formation 110. One ofordinary skill in the art would appreciate from the present disclosurethat the order of these steps is for illustration only and otherpermutations are possible without departing from the scope of theinvention. For example, the data needed to characterize the drillingoperation may be provided after the construction of the mechanicsanalysis model

In one example, illustrated in FIG. 4, solving for the dynamic response116 may not only include solving the mechanics analysis model for thedynamic response to an incremental rotation 120, but may also includedetermining, from the response obtained, loads (e.g., drillingenvironment interaction forces, bending moments, etc.) on the drillingtool assembly due to interactions between the drilling tool assembly andthe drilling environment during the incremental rotation 122, andresolving for the response of the drilling tool assembly to theincremental rotation 124 under the newly determined loads. Thedetermining and resolving may be repeated in a constraint update loop128 until a response convergence criterion 126 is satisfied.

For example, assuming the simulation is performed under a constant WOB,with each incremental rotation, the drill bit is rotated by a smallangle and moved downward (axially) by a small distance. During thismovement, the interference between the drill bit and the bottom of thehole generates counter force acting against the drill bit (loads). Ifthe load is more than the WOB, then the rotation or downward movement ofthe drill bit is too much. The parameters (constraints) should beadjusted (e.g., reduced the downward movement distance) and theincremental rotation is again performed. On the other hand, if the loadafter the incremental rotation is less than the WOB, then theincremental rotation should be performed with a larger angular or axialmovement.

Once a convergence criterion is satisfied, the entire incrementalsolving process 116 may be repeated for successive increments until anend condition for simulation is reached. These steps (incrementalrotation, load calculation, comparison with a criterion, and adjustmentof constraints) are repeated until the computed load from theincremental rotation is within a selected criterion (step 126). Once aconvergence criterion is satisfied, the entire incremental solvingprocess 116 may be repeated for successive increments 129 until an endcondition for simulation is reached.

During the simulation, the constraint forces initially used for each newincremental calculation step may be the constraint forces determinedduring the last incremental rotation. In the simulation, incrementalrotation and calculations are repeated for a select number of successiveincremental rotations until an end condition for simulation is reached.

As shown in FIG. 5A-B, the parameters provided as input 200 includedrilling tool assembly design parameters 202, initial drillingenvironment parameters 204 and drilling operation parameters 206.Drilling tool assembly/drilling environment interaction parameters arealso provided or selected as input 208.

Drilling tool assembly design parameters 202 include drill string designparameters and BHA design parameters. The drill string can be defined asa plurality of segments of drill pipe with tool joints and the BHA maybe defined as including a number of drill collars, stabilizers, andother downhole components, such as a bent housing motor, MWD tool, LWDtool, thruster, point the bit directional drilling tool, push the bitdirectional drilling tool, shock absorber, point stab, and a drill bit.One or more of these items may be selected from a library list of toolsand used in the design of a drilling tool assembly model, as shown inFIG. 5A. Also, while the drill bit is generally considered part of theBHA, the drill bit design parameters may be defined in a bit parameterinput screen and used separately in a detailed modeling of bitinteraction with the earth formation that can be coupled to the drillingtool assembly design model and described below. Considering the detailedinteraction of the bit with the earth formation separately in a bitcalculation subroutine coupled to the drilling tool assembly modeladvantageously allows for the interchangeable use of any type of drillbit which can be defined and modeled using any desired drill bitanalysis model. The calculated response of the bit interacting with theformation is coupled to the drilling tool assembly design model so thatthe effect of the selected drill bit interacting with the formationduring drilling can be directly determined for the selected drillingtool assembly.

As previously discussed above, drill string design parameters mayinclude the length, inside diameter (ID), outside diameter (OD), weight(or density), and other material properties of the drill string in theaggregate. Alternatively, in one or more embodiments, drill stringdesign parameters may include the properties of each component of thedrill string and the number of components and location of each componentof the drill string. In the example shown in FIG. 8, the length, ID, OD,weight, and material properties of a segment of drill pipe may beprovided as input along with the number of segments of drill pipe thatmake up the drill string. Material properties of the drill stringprovided as input may also include the type of material and/or thestrength, elasticity and density of the material. The weight of thedrill string, or individual segment of the drill string may be providedas its “air” weight or as “weight in drilling fluids” (the weight of thecomponent when submerged in the selected drilling fluid).

In accordance with one or more embodiments of the invention, the drillstring need not be represented in true relative dimensions in thesimulation. Instead, the drill string may be represented as sections(nodes) of different lengths. For example, the nodes closer to the BHAand drill bit may be represented as shorter sections (closer nodes) inorder to better define the dynamics of the drill string close to thedrill bit. On the other hand, drill string sections farther away fromthe BHA may be represented as longer sections (far apart nodes) in thesimulation to save the computer resources.

BHA design parameters include, for example, the bent angle andorientation of the motor, the length, equivalent inside diameter (ID),outside diameter (OD), weight (or density), and other materialproperties of each of the various components of the BHA. In the exampleshown, the drill collars, stabilizers, and other downhole components aredefined by their lengths, equivalent IDs, ODs, material properties, andeccentricity of the various parts, their weight in drilling fluids, andtheir position in the drilling tool assembly recorded.

Drill bit design parameters are also provided as input and used toconstruct a model for the selected drill bit. Drill bit designparameters include, for example, the bit type such as a fixed-cutterdrill bit and geometric parameters of the bit. Geometric parameters ofthe bit may include the bit size (e.g., diameter), number of cuttingelements, and the location, shape, size, and orientation of the cuttingelements. In the case of a fixed cutter bit, the drill bit designparameters may further include the size of the bit, parameters definingthe profile and location of each of the blades on the cutting face ofthe drill bit, the number and location of cutting elements on eachblade, the back rake and side rake angles for each cutting element. Ingeneral, drill bit, cutting element, and cutting structure geometry maybe converted to coordinates and provided as input to the simulationprogram. In one or more embodiments, the method used for obtaining bitdesign parameters involves uploading of 3-dimensional CAD solid orsurface model of the drill bit to facilitate the geometric input. Drillbit design parameters may further include material properties of thevarious components that make up the drill bit, such as strength,hardness, and thickness of various materials forming the cuttingelements, blades, and bit body.

In one or more embodiments, drilling environment parameters 204 includeone or more parameters characterizing aspects of the wellbore. Wellboreparameters may include wellbore trajectory parameters and wellboreformation parameters. Wellbore trajectory parameters may include anyparameter used in characterizing a wellbore trajectory, such as aninitial wellbore depth (or length), diameter, inclination angle, andazimuth direction of the trajectory or a segment of the trajectory. Inthe typical case of a wellbore comprising different segments havingdifferent diameters or directional orientations, wellbore trajectoryparameters may include depths, diameters, inclination angles, andazimuth directions for each of the various segments. Wellbore trajectoryinformation may also include an indication of the curvature of eachsegment, and the order or arrangement of the segments in wellbore.Wellbore formation parameters may also include the type of formationbeing drilled and/or material properties of the formation such as theformation compressive strength, hardness, plasticity, and elasticmodulus. An initial bottom surface of the wellbore may also be providedor selected as input. The bottomhole geometry may be defined as flat orcontour and provided as wellbore input. Alternatively, the initialbottom surface geometry may be generated or approximated based on theselected bit geometry. For example, the initial bottomhole geometry maybe selected from a “library” (i.e., database) containing storedbottomhole geometries resulting from the use of various drill bits.

In one or more embodiments, drilling operation parameters 206 includethe rotary speed (RPM) at which the drilling tool assembly is rotated atthe surface and/or a downhole motor speed if a downhole motor is used.The drilling operation parameters also include a weight on bit (WOB)parameter, such as hook load, or a rate of penetration (ROP). Otherdrilling operation parameters 206 may include drilling fluid parameters,such as the viscosity and density of the drilling fluid, rotary torqueand drilling fluid flow rate. The drilling operating parameters 206 mayalso include the number of bit revolutions to be simulated or thedrilling time to be simulated as simulation ending conditions to controlthe stopping point of simulation. However, such parameters are notnecessary for calculation required in the simulation. In otherembodiments, other end conditions may be provided, such as a totaldrilling depth to be simulated or operator command.

In one or more embodiments, input is also provided to determine thedrilling tool assembly/drilling environment interaction models 208 to beused for the simulation. As discussed in U.S. Pat. No. 6,516,293 andU.S. Provisional Application No. 60/485,642, cutting element/earthformation interaction models may include empirical models or numericaldata useful in determining forces acting on the cutting elements basedon calculated displacements, such as the relationship between a cuttingforce acting on a cutting element, the corresponding scraping distanceof the cutting element through the earth formation, and the relationshipbetween the normal force acting on a cutting element and thecorresponding depth of penetration of the cutting element in the earthformation. Cutting element/earth formation interaction models may alsoinclude wear models for predicting cutting element wear resulting fromprolonged contact with the earth formation, cutting structure/formationinteraction models and bit body/formation interaction models fordetermining forces on the cutting structure and bit body when they aredetermined to interact with earth formation during drilling. In one ormore embodiments, coefficients of an interaction model may be adjustableby a user to adapt a generic model to more closely fit characteristicsof interaction as seen during drilling in the field. For example,coefficients of the wear model may be adjustable to allow for the wearmodel to be adjusted by a designer to calculate cutting element wearmore consistent with that found on dull bits run under similarconditions.

Drilling tool assembly/earth formation impact, friction, and dampingmodels or parameters can be used to characterize impact and friction onthe drilling tool assembly due to contact of the drilling tool assemblywith the wall of the wellbore and due to viscous damping effects of thedrilling fluid. These models may include drill string-BHA/formationimpact models, bit body/formation impact models, drillstring-BHA/formation friction models, and drilling fluid viscous dampingmodels. One skilled in the art will appreciate that impact, friction anddamping models may be obtained through laboratory experimentation.Alternatively, these models may also be derived based on mechanicalproperties of the formation and the drilling tool assembly, or may beobtained from literature. Prior art methods for determining impact andfriction models are shown, for example, in papers such as the one by YuWang and Matthew Mason, entitled “Two-Dimensional Rigid-Body Collisionswith Friction,” Journal of Applied Mechanics, September 1992, Vol. 59,pp. 635-642.

Input data may be provided as input to a simulation program by way of auser interface which includes an input device coupled to a storagemeans, a database and a visual display, wherein a user can select whichparameters are to be defined, such as operation parameters, drill stringparameters, well parameters, and etc. Then, once the type of parametersto be defined is selected, the user selected the component or valuedesired to be changed and enter or select a changed value for use inperforming the simulation.

In one or more embodiments, the user may select to change simulationparameters, such as the type of simulation mode desired (such as fromROP control to WOB control, etc.), or various calculation parameters,such as impact model modes (force, stiffness, etc.), bending-torsionmodel modes (coupled, decoupled), damping coefficients model,calculation incremental step size, etc. The user may also select todefine and modify drilling tool assembly parameters. The user mayconstruct a drilling tool assembly to be simulated by selecting thecomponent to be included in the drilling tool assembly from a databaseof components and by adjusting the parameters for each of the componentsas needed to create a drilling tool assembly model that very closelyrepresents the actual drilling tool assembly being considered for use.

In one embodiment, the specific parameters for each component selectedfrom the database may be adjustable, for example, by selecting acomponent added to the drilling tool assembly and changing the geometricor material property values defined for the component in a menu screenso that the resulting component selected more closely matches with theactual component included in the actual drilling tool assembly. Forexample, in one embodiment, a stabilizer in the drilling tool assemblymay be selected and any one of the overall length, outside bodydiameter, inside body diameter, weight, blade length, blade OD, bladewidth, number of blades, thickness of blades, eccentricity offset, andeccentricity angle may be provided as well as values relating to thematerial properties (e.g., Young's modulus, Poisson's ratio, etc.) ofthe tool may be specifically defined to more accurately represent thestabilizer to be used in the drilling tool assembly being modeled.Similar features may also be provided for each of the drill collars,drill pipe, cross over subs, etc., included in the drilling toolassembly. In the case of drill pipe, and similar components, additionalfeatures defined may include the length and outside diameter of eachtool connection joint, so that the effect of the actual tool joints onstiffness and mass throughout the system can be taken into accountduring calculations to provide a more accurate prediction of the dynamicresponse of the drilling tool assembly being modeled.

The user may also select and define the well by selecting well surveydata and wellbore data. For example, for each segment a user may definethe measured depth, inclination angle, and azimuth angle of each segmentof the wellbore, and the diameter, well stiffness, coefficient ofrestitution, axial and transverse damping coefficients of friction,axial and transverse scraping coefficient of friction, and mud density.

Constructing the Model

As shown in FIG. 5A-B, once input data 200 are selected, determined, orotherwise provided, a two-part mechanics analysis model of the drillingtool assembly may be constructed 210 and used to determine the initialstatic state 212 of the drilling tool assembly in the wellbore. Thefirst part of the mechanics analysis model construction 210 takes intoconsideration the overall structure of the drilling tool assembly, withthe drill bit being only generally represented. In this embodiment, afinite element method is used (generally described at 212), wherein anarbitrary initial state (such as hanging in the vertical mode free ofbending stresses) is defined for the drilling tool assembly as areference and the drilling tool assembly is divided into N elements ofspecified element dimensions (i.e., meshed). The static load vector foreach element due to gravity is calculated. Then, element stiffnessmatrices are constructed based on the material properties, elementlength, and cross sectional geometrical properties of drilling toolassembly components provided as input for the entire drilling toolassembly (wherein the drill bit is generally represented by a singlenode). Similarly, element mass matrices are constructed by determiningthe mass of each element (based on material properties, etc.) for theentire drilling tool assembly 214. Additionally, element dampingmatrices can be constructed (based on experimental data, approximation,or other method) for the entire drilling tool assembly 216. Methods fordividing a system into finite elements and constructing correspondingstiffness, mass, and damping matrices are known in the art and thus arenot explained in detail here. Examples of such methods are shown, forexample, in “Finite Elements for Analysis and Design” by J. E. Akin(Academic Press, 1994).

The second part of the mechanics analysis model 210 of the drilling toolassembly is a mechanics analysis model of the drill bit 218 which takesinto account details of selected drill bit design. The drill bitmechanics analysis model 218 may be constructed by creating a mesh (or asurface model or a solid model) of the cutting elements and establishinga coordinate relationship (coordinate system transformation) between thecutting elements and the bit, and between the bit and the tip of theBHA. As previously noted, examples of methods for constructing mechanicsanalysis models for fixed cutter bits are disclosed in SPE Paper No.15618 by T. M. Warren et al., entitled “Drag Bit Performance Modeling,”U.S. Pat. No. 4,815,342, U.S. Pat. No. 5,010,789, U.S. Pat. No.5,042,596, and U.S. Pat. No. 5,131,479 to Brett et al, and U.S.Provisional Application No. 60/485,642.

For each incremental rotation, the method may include calculating cutterwear based on forces on the cutters, the interference of the cutterswith the formation, and a wear model and modifying cutter shapes basedon the calculated cutter wear. These steps may be inserted into themethod at the point indicated by the node labeled “A.”

Further, those having ordinary skill will appreciate that the work doneby the bit and/or individual cutters may be determined. Work is equal toforce times distance, and because embodiments of the simulation provideinformation about the force acting on a cutter and the distance into theformation that a cutter penetrates, the work done by a cutter may bedetermined.

Other implementations of a method developed in accordance with thisaspect of the invention may include a drilling model based on ROPcontrol. Other implementations may include a drilling model based uponWOB control. Generally speaking the method includes selecting orotherwise inputting parameters for a dynamic simulation. Parametersprovided as input include drilling parameters, bit design parameters,cutter/formation interaction data and cutter wear data, and bottomholeparameters for determining the initial bottomhole shape. The data andparameters provided as input for the simulation can be stored in aninput library and retrieved as needed during simulation calculations.

Drilling parameters may include any parameters that can be used tocharacterize drilling. In the method shown, the drilling parametersprovided as input include the rate of penetration (ROP) or the weight onbit (WOB) and the rotation speed of the drill bit (revolutions perminute, RPM). Those having ordinary skill in the art would recognizethat other parameters (e.g., mud weight) may be included.

Bit design parameters may include any parameters that can be used tocharacterize a bit design. In the method shown, bit design parametersprovided as input include the cutter locations and orientations (e.g.,radial and angular positions, heights, profile angles, back rake angles,side rake angles, etc.) and the cutter sizes (e.g., diameter), shapes(i.e., geometry) and bevel size. Additional bit design parameters mayinclude the bit profile, bit diameter, number of blades on bit bladegeometries, blade locations, junk slot areas, bit axial offset (from theaxis of rotation), cutter material make-up (e.g., tungsten carbidesubstrate with hardfacing overlay of selected thickness), etc. Thoseskilled in the art will appreciate that cutter geometries and the bitgeometry can be meshed, converted to coordinates and provided asnumerical input. Preferred methods for obtaining bit design parametersfor use in a simulation include the use of 3-dimensional CAD solid orsurface models for a bit to facilitate geometric input.

Cutter/formation interaction data includes data obtained fromexperimental tests or numerically simulations of experimental testswhich characterize the actual interactions between selected cutters andselected earth formations, as previously described in detail above. Weardata may be data generated using any wear model known in the art or maybe data obtained from cutter/formation interaction tests that includedan observation and recording of the wear of the cutters during the test.A wear model may comprise a mathematical model that can be used tocalculate an amount of wear on the cutter surface based on forces on thecutter during drilling or experimental data which characterizes wear ona given cutter as it cuts through the selected earth formation. U.S.Pat. No. 6,619,411 issued to Singh et al. discloses methods for modelingwear of roller cone drill bits. This patent is assigned to the presentassignee and is incorporated by reference in its entirety. Wear modelingfor fixed cutter bits (e.g., PDC bits) will be described in a latersection. Other patents related to wear simulation include U.S. Pat. Nos.5,042,596, 5,010,789, 5,131,478, and 4,815,342. The disclosures of thesepatents are incorporated by reference in their entireties.

Bottomhole parameters used to determine the bottomhole shape may includeany information or data that can be used to characterize the initialgeometry of the bottomhole surface of the well bore. The initialbottomhole geometry may be considered as a planar surface, but this isnot a limitation on the invention. Those skilled in the art willappreciate that the geometry of the bottomhole surface can be meshed,represented by a set of spatial coordinates, and provided as input. Inone implementation, a visual representation of the bottomhole surface isgenerated using a coordinate mesh size of 1 millimeter.

Once the input data is entered or otherwise made available and thebottomhole shape determined, the steps in a main simulation loop can beexecuted. Within the main simulation loop, drilling is simulated by“rotating” the bit (numerically) by an incremental amount, Δθ_(bit,i).The rotated position of the bit at any time can be expressed as,

$\begin{matrix}{\theta_{bit} = {\sum\limits^{i}{\Delta\;{\theta_{{bit},i}.}}}} & (1)\end{matrix}$Δθ_(bit,i), may be set equal to 3 degrees, for example. In otherimplementations, Δθ_(bit,i), may be a function of time or may becalculated for each given time step. The new location of each of thecutters is then calculated, based on the known incremental rotation ofthe bit, Δθ_(bit,i), and the known previous location of each of thecutters on the bit. At this step, the new cutter locations only reflectthe change in the cutter locations based on the incremental rotation ofthe bit. The newly rotated location of the cutters can be determined bygeometric calculations known in the art. The axial displacement of thebit, Δd_(bit,i), resulting for the incremental rotation, Δθ_(bit,i), maybe determined using an equation such as:

$\begin{matrix}{{\Delta\; d_{{bit},i}} = {\frac{\left( {{ROP}_{i}/{RPM}_{i}} \right)}{60} \cdot {\left( {\Delta\;\theta_{{bit},i}} \right)/360.}}} & (2)\end{matrix}$

Once the axial displacement of the bit, Δd_(bit,i), is determined, thebit is “moved” axially downward (numerically) by the incrementaldistance, Δd_(bit,i), (with the cutters at their newly rotatedlocations). Then the new location of each of the cutters after the axialdisplacement is calculated. The calculated location of the cutters nowreflects the incremental rotation and axial displacement of the bitduring the “increment of drilling.” Then, the interference of eachcutter with the bottomhole is determined. Determining cutterinteractions with the bottomhole includes calculating the depth of cut,the interference surface area, and the contact edge length for eachcutter contacting the formation during the increment of drilling by thebit. These cutter/formation interaction parameters can be calculatedusing geometrical calculations known in the art.

Once the correct cutter/formation interaction parameters are determined,the axial force on each cutter (in the Z direction with respect to a bitcoordinate system as illustrated in FIG. 8) during increment drillingstep, i, is determined. The force on each cutter is determined from thecutter/formation interaction data based on the calculated values for thecutter/formation interaction parameters and cutter and formationinformation.

Referring to FIG. 8, the normal force, cutting force, and side force oneach cutter is determined from cutter/formation interaction data basedon the known cutter information (cutter type, size, shape, bevel size,etc.), the selected formation type, the calculated interferenceparameters (i.e., interference surface area, depth of cut, contact edgelength) and the cutter orientation parameters (i.e., back rake angle,side rake angle, etc.). For example, the forces may be determined byaccessing a cutter/formation interaction database for a cutter andformation pair similar to the cutter and earth formation interactionduring drilling. Then, the values calculated for the interactionparameters (depth of cut, interference surface area, contact edgelength, back rack, side rake, and bevel size) during drilling are usedto look up the forces required on the cutter to cut through formation inthe cutter/formation interaction database. If values for the interactionparameters do not match values contained in the cutter/formationinteraction database, records containing the most similar parameters areused and values for these most similar records can be used tointerpolate the force required on the cutting element during drilling.

The displacement of each of the cutters is calculated based on theprevious cutter location. The forces on each cutter are then determinedfrom cutter/formation interaction data based on the cutter lateralmovement, penetration depth, interference surface area, contact edgelength, and other bit design parameters (e.g., back rake angle, siderake angle, and bevel size of cutter). Cutter wear is also calculatedfor each cutter based on the forces on each cutter, the interactionparameters, and the wear data for each cutter. The cutter shape ismodified using the wear results to form a worn cutter for subsequentcalculations.

FIG. 9A shows a single cutter 295 in an example of a modeled positionfor engaging a formation 296 and FIGS. 9B and 9C show force orientationand nomenclature for discussion purposes. The back rake angle α_(br) isshown at 291 in FIG. 9A and the side rake angle α_(sr) is shown at 293in FIG. 9C. Once the forces, for example F_(N), F_(cut), and F_(side)(see FIG. 9B), on each of the cutters during the incremental drillingstep are determined. These forces may be resolved into bit coordinatesystem, O_(ZRθ), illustrated in FIG. 8, (axial (Z), radial (R), andcircumferential (C) that is perpendicular into the page in FIG. 8).Then, all of the forces on the cutters in the axial direction are summedto obtain a total axial force F_(Z) on the bit. The axial force requiredon the bit during the incremental drilling step is taken as the weighton bit (WOB) required to achieve the given ROP or alternatively the ROPrequired to achieve a given WOB is determined.

The total force required on the cutter to cut through earth formationcan be resolved into components in any selected coordinate system, suchas the Cartesian coordinate system shown in FIGS. 9A-C and 10A-C. Asshown in FIG. 9B, the force on the cutter can be resolved into a normalcomponent (normal force), F_(N), a cutting direction component (cutforce), F_(cut), and a side component (side force), F_(side). In thecutter coordinate system shown in FIG. 9B, the cutting axis ispositioned along the direction of cut. The normal axis is normal to thedirection of cut and generally perpendicular to the surface of the earthformation 296 interacting with the cutter. The side axis is parallel tothe surface of the earth formation 296 and perpendicular to the cuttingaxis. The origin of this cutter coordinate system is shown positioned atthe center of the cutter 295.

The bottomhole pattern is updated. The bottomhole pattern can be updatedby removing the formation in the path of interference between thebottomhole pattern resulting from the previous incremental drilling stepand the path traveled by each of the cutters during the currentincremental drilling step.

Output information, such as forces on cutters, weight on bit, and cutterwear, may be provided for further analysis. The output information mayinclude any information or data which characterizes aspects of theperformance of the selected drill bit drilling the specified earthformations. For example, output information can include forces acting onthe individual cutters during drilling, scraping movement/distance ofindividual cutters on the hole bottom and on the hole wall, total forcesacting on the bit during drilling, and the weight on bit to achieve theselected rate of penetration for the selected bit. Output informationmay be used to generate a visual display of the results of the drillingsimulation. The visual display can include a graphical representation ofthe well bore being drilled through earth formations. The visual displaycan also include a visual depiction of the earth formation being drilledwith cut sections of formation calculated as removed from the bottomholeduring drilling being visually “removed” on a display screen. The visualrepresentation may also include graphical displays of forces, such as agraphical display of the forces on the individual cutters, on the bladesof the bit, and on the drill bit during the simulated drilling. Thevisual representation may also include graphical displays force angles,Beta angle separation between force components, and historic or timedependent depictions of forces and angles. The means, whether a graph, avisual depiction or a numerical table used for visually displayingaspects of the drilling performance can be a matter of choice for thesystem designer, and is not a limitation on the invention. According toone aspect of the invention, it is useful to display the Beta anglebetween cut direction component of the total of imbalance force and theradial direction component of the total imbalance force during a periodof time of simulated drilling.

As should be understood by one of ordinary skill in the art, withreference to co-owned, co-pending U.S. patent application Ser. No.10/888,446, incorporated herein by reference in its entirety, the stepswithin a main simulation loop are repeated as desired by applying asubsequent incremental rotation to the bit and repeating thecalculations in the main simulation loop to obtain an updated cuttergeometry (if wear is modeled) and an updated bottomhole geometry for thenew incremental drilling step. Repeating the simulation loop asdescribed above will result in the modeling of the performance of theselected fixed cutter drill bit drilling the selected earth formationsand continuous updates of the bottomhole pattern drilled. In this way,the method as described can be used to simulate actual drilling of thebit in earth formations.

An ending condition, such as the total depth to be drilled, can be givenas a termination command for the simulation, the incremental rotationand displacement of the bit with subsequent calculations in thesimulation loop will be repeated until the selected total depth drilledis reached, as calculated below:

$\begin{matrix}{D = {\sum\limits^{i}{\Delta\;{d_{{bit},i}.}}}} & (3)\end{matrix}$Alternatively, the drilling simulation can be stopped at any time usingany other suitable termination indicator, such as a selected input froma user or a desired output from the simulation.

Embodiments of the present invention advantageously provide the abilityto model inhomogeneous regions and transitions between layers. Withrespect to inhomogeneous regions, sections of formation may be modeledas nodules or beams of different material embedded into a base material,for example. That is, a user may define a section of a formation asincluding various non-uniform regions, whereby several different typesof rock are included as discrete regions within a single section.

Returning to FIGS. 5A-C, in accordance with some embodiments of theinvention, wellbore constraints for the drilling tool assembly may bedetermined, at 222, 224, because the response of the drilling toolassembly is subject to the constraint within the wellbore. First, thetrajectory of the wall of the wellbore, which constrains the drillingtool assembly and forces it to conform to the wellbore path, isconstructed at 220 using wellbore trajectory parameters provided asinput at 204. For example, a cubic B-spline method or otherinterpolation method can be used to approximate wellbore wallcoordinates at depths between the depths provided as input data. Thewall coordinates are then discretized (or meshed), at 224 and stored.Similarly, an initial wellbore bottom surface geometry, which is eitherselected or determined, is also discretized, at 222, and stored. Theinitial bottom surface of the wellbore may be selected as flat or as anyother contour, which can be provided as wellbore input at 204 or 222.Alternatively, the initial bottom surface geometry may be generated orapproximated based on the selected bit geometry. For example, theinitial bottomhole geometry may be selected from a “library” (i.e.,database) containing stored bottomhole geometries resulting from the useof various bits.

In the example embodiment shown in FIG. 5A, a coordinate mesh size of 1millimeter is selected for the wellbore surfaces (wall and bottomhole);however, the coordinate mesh size is not intended to be a limitation onthe invention. Once meshed and stored, the wellbore wall and bottomholegeometry, together, comprise the initial wellbore constraints withinwhich the drilling tool assembly operates, and, thus, within which thedrilling tool assembly response is constrained.

Once the mechanics analysis model for the drilling tool assemblyincluding the bit is constructed 210 and the wellbore constraints arespecified 222, 224, the mechanics model and constraints can be used todetermine the constraint forces on the drilling tool assembly whenforced to the wellbore trajectory and bottomhole from its original“stress free” state. In this embodiment, the constraint forces on thedrilling tool assembly are determined by first displacing and fixing thenodes of the drilling tool assembly so the centerline of the drillingtool assembly corresponds to the centerline of the wellbore, at 226.Then, the corresponding constraining forces required on each node (tofix it in this position) are calculated at 228 from the fixed nodaldisplacements using the drilling tool assembly (i.e., system or global)stiffness matrix from 212. Once the “centerline” constraining forces aredetermined, the hook load is specified, and initial wellbore wallconstraints and bottomhole constraints are introduced at 230 along thedrilling tool assembly and at the bit (lowest node). The centerlineconstraints are used as the wellbore wall constraints. The hook load andgravitational force vector are used to determine the WOB.

As previously noted, the hook load is the load measured at the hook fromwhich the drilling tool assembly is suspended. Because the weight of thedrilling tool assembly is known, the bottomhole constraint force (i.e.,WOB) can be determined as the weight of the drilling tool assembly minusthe hook load and the frictional forces and reaction forces of the holewall on the drilling tool assembly.

Once the initial loading conditions are introduced, the “centerline”constraint forces on all of the nodes may be removed, a gravitationalforce vector may be applied, and the static equilibrium position of theassembly within the wellbore may be determined by iterativelycalculating the static state of the drilling tool assembly 232.Iterations are necessary since the contact points for each iteration maybe different. The convergent static equilibrium state is reached and theiteration process ends when the contact points and, hence, contactforces are substantially the same for two successive iterations. Alongwith the static equilibrium position, the contact points, contactforces, friction forces, and static WOB on the drilling tool assemblymay be determined. Once the static state of the system is obtained, itcan be used as the staring point for simulation of the dynamic responseof the drilling tool assembly drilling earth formation 234.

During the simulation, the constraint forces initially used for each newincremental calculation step may be the constraint forces determinedduring the last incremental rotation. In the simulation, incrementalrotation calculations are repeated for a select number of successiveincremental rotations until an end condition for simulation is reached.

As shown in FIG. 5A-C, once input data are provided and the static stateof the drilling tool assembly in the wellbore is determined,calculations in the dynamic response simulation loop 240 can be carriedout. Briefly summarizing the functions performed in the dynamic responseloop 240, the drilling tool assembly drilling earth formation issimulated by “rotating” the top of the drilling tool assembly (and atthe location corresponding to a downhole motor, if used) through anincremental angle (at 242) corresponding to a selected time incrementand then calculating the response of the drilling tool assembly underthe previously determined loading conditions 244 to the incrementalrotation(s). The constraint loads on the drilling tool assemblyresulting from interaction with the wellbore wall during the incrementalrotation are iteratively determined (in loop 245) and are used to updatethe drilling tool assembly constraint loads (i.e., global load vector),at 248, and the response is recalculated under the updated loadingcondition. The new response is then rechecked to determine if wallconstraint loads have changed and, if necessary, wall constraint loadsare re-determined, the load vector updated, and a new responsecalculated. Then, the bottomhole constraint loads resulting from bitinteraction with the formation during the incremental rotation areevaluated based on the new response (at 252), the load vector is updated(at 279), and a new response is calculated (at 280). The wall andbottomhole constraint forces are repeatedly updated (in loop 285) untilconvergence of a dynamic response solution is obtained (i.e., changes inthe wall constraints and bottomhole constraints for consecutivesolutions are determined to be negligible). The entire dynamicsimulation loop 240 is then repeated for successive incrementalrotations until an end condition of the simulation is reached (at 290)or until simulation is otherwise terminated. A more detailed descriptionof the elements in the simulation loop 240 follows.

Prior to the start of the simulation loop 240, drilling operationparameters 206 are specified. As previously noted, the drillingoperation parameters 206 may include the rotary table speed, downholemotor speed (if a downhole motor is included in the BHA), rate ofpenetration (ROP), and the hook load (and/or other weight on bitparameter). In this example, the end condition for simulation is alsoprovided at 206, as either the total number of revolutions to besimulated or the total time for the simulation. Additionally, theincremental step desired for calculations should be defined, selected,or otherwise provided. In the embodiment shown, an incremental time stepof Δt=10⁻³ seconds is selected. However, it should be understood thatthe incremental time step is not intended to be a limitation on theinvention.

Once the static state of the system is known (from 232) and theoperational parameters are provided, the dynamic response simulationloop 240 can begin. First, the current time increment is calculated at241, wherein:t _(i+1) =t _(i) +Δt.  (4)Then, the incremental rotation occurring during that time increment iscalculated at 242. In this embodiment, RPM is considered an inputparameter. Therefore, the formula used to calculate the incrementalrotation angle at time t_(i+1) is:Δθ_(i+1)=RPM*360*Δt/60,  (5)wherein RPM is the rotational speed (in RPM) of the rotary table or topdrive provided as input data (at 206). The calculated incrementalrotation angle is applied proximal to the top of the drilling toolassembly (at the node(s) corresponding to the position of the rotarytable). If a downhole motor is included in the BHA, the downhole motorincremental rotation is also calculated and applied at the nodescorresponding to the downhole motor.

Once the incremental rotation angle and current time are determined, thesystem's new configuration (nodal positions) under the extant loads andthe incremental rotation is calculated (at 244) using the drilling toolassembly mechanics analysis model and the rotational input as anexcitation. A direct integration scheme can be used to solve theresulting dynamic equilibrium equations for the drilling tool assembly.The dynamic equilibrium equation (like the mechanics analysis equation)can be derived using Newton's second law of motion, wherein theconstructed drilling tool assembly mass, stiffness, and damping matricesalong with the calculated static equilibrium load vector can be used todetermine the response to the incremental rotation. For the exampleshown in FIG. 5A-C, it should be understood that at the first timeincrement t₁ the extant loads on the system are the static equilibriumloads (calculated for to) which include the static state WOB and theconstraint loads resulting from drilling tool assembly contact with thewall and bottom of the wellbore.

As the drilling tool assembly is incrementally “rotated,” constraintloads acting on the bit may change. For example, points of the drillingtool assembly in contact with the borehole surface prior to rotation maybe moved along the surface of the wellbore resulting in friction forcesat those points. Similarly, some points of the drilling tool assembly,which were close to contacting the borehole surface prior to theincremental rotation, may be brought into contact with the formation asa result of the incremental rotation. This may result in impact forceson the drilling tool assembly at those locations. As shown in FIG. 5A-C,changes in the constraint loads resulting from the incremental rotationof the drilling tool assembly can be accounted for in the wallinteraction update loop 245.

In the example shown, once the system's response (i.e., newconfiguration) under the current loading conditions is obtained, thepositions of the nodes in the new configuration are checked at 246 inthe wall constraint loop 245 to determine whether any nodaldisplacements fall outside of the bounds (i.e., violate constraintconditions) defined by the wellbore wall. If nodes are found to havemoved outside of the wellbore wall, the impact and/or friction forceswhich would have occurred due to contact with the wellbore wall areapproximated for those nodes at 248 using the impact and/or frictionmodels or parameters provided as input at 208. Then the global loadvector for the drilling tool assembly is updated, also at 248, toreflect the newly determined constraint loads. Constraint loads to becalculated may be determined to result from impact if, prior to theincremental rotation, the node was not in contact with the wellborewall. Similarly, the constraint load can be determined to result fromfrictional drag if the node now in contact with the wellbore wall wasalso in contact with the wall prior to the incremental rotation. Oncethe new constraint loads are determined and the global load vector isupdated, at 248, the drilling tool assembly response is recalculated (at244) for the same incremental rotation under the newly updated loadvector (as indicated by loop 245). The nodal displacements are thenrechecked (at 246) and the wall interaction update loop 245 is repeateduntil a dynamic response within the wellbore constraints is obtained.

Once a dynamic response conforming to the borehole wall constraints isdetermined for the incremental rotation, the constraint loads on thedrilling tool assembly due to interaction with the bottomhole during theincremental rotation are determined in the bit interaction loop 250.Those skilled in the art will appreciate that any method for modelingdrill bit/earth formation interaction during drilling may be used todetermine the forces acting on the drill bit during the incrementalrotation of the drilling tool assembly. An example of one method isillustrated in the bit interaction loop 250 in FIG. 5B.

In the bit interaction loop 250, the mechanics analysis model of thedrill bit is subjected to the incremental rotation angle calculated forthe lowest node of the drilling tool assembly, and is then movedlaterally and vertically to the new position obtained from the samecalculation, as shown at 249. As previously noted, the drill bit in thisexample is a fixed cutter drill bit. The interaction of the drill bitwith the earth formation is modeled in accordance with a methoddisclosed in U.S. Provisional Application No. 60/485,642, which has beenincorporated herein by reference. Thus, in this example, once therotation and new position for the bit node are known, they are used asinput to the drill bit model and the drill bit model is used tocalculate the new position for each of the cutting elements on the drillbit. Then, the location of each cutting element relative to thebottomhole and wall of the wellbore is evaluated, at 254, to determinefor each cutting element whether cutting element interference with theformation occurred during the incremental movement of the bit.

If cutting element contact is determined to have occurred with the earthformation, surface contact area between the cutter and the earthformation is calculated along with the depth of cut and the contact edgelength of the cutter, and the orientation of the cutting face withrespect to the formation (e.g., back rake angle, side rake angle, etc.)at 264. The depth of cut is the depth below the formation surface that acutting element contacts earth formation, which can range from zero (nocontact) to the full height of the cutting element. Surface area contactis the fractional amount of the cutting surface area out of the entirearea corresponding to the depth of cut that actually contacts earthformation. This may be a fractional amount of contact due to cuttingelement grooves formed in the formation from previous contact withcutting elements. The contact edge length is the distance betweenfarthest points on the edge of the cutter in contact with formation atthe formation surface. Scraping distance takes into account the movementof the cutting element in the formation during the incremental rotation.

Once the depth of cut, surface contact area, contact edge length, andscraping distance are determined for a cutting element these parameterscan be stored and used along with the cutting element/formationinteraction data to determine the resulting forces acting on the cuttingelement during the incremental movement of the bit (also indicated at264). For example, in accordance a simulation method described in U.S.Provisional Application No. 60/485,642 noted above, resulting forces oneach of the cutters can be determined using cutter/formation interactiondata stored in a data library involving a cutter and formation pairsimilar to the cutter and earth formation interacting during thesimulated drilling. Values calculated for interaction parameters (depthof cut, interference surface area, contact edge length, back rack, siderake, and bevel size) during drilling are used to determine thecorresponding forces required on the cutters to cut through the earthformation. In cases where the cutting element makes less than fullcontact with the earth formation due to grooves in the formationsurface, an equivalent depth of cut and equivalent contact edge lengthmay be calculated to correspond to the interference surface area andthese values are used to determine the forces required on the cuttingelement during drilling.

Once the cutting element/formation interaction variables (contact area,depth of cut, force, etc.) are determined for cutting elements, thegeometry of the bottom surface of the wellbore is temporarily updated,to reflect the removal of formation by each cutting element during theincremental rotation of the drill bit.

After the bottomhole geometry is temporarily updated, insert wear andstrength can also be analyzed, as shown at 258, based on wear models andcalculated loads on the cutting elements to determine wear on thecutting elements resulting from contact with the formation and theresulting reduction in cutting element strength.

As noted above, cutter wear is a function of the force exerted on thecutter. In addition, other factors that may influence the rates ofcutter wear include the velocity of the cutter brushing against theformation (i.e., relative sliding velocity), the material of the cutter,the area of the interference or depth of cut (d), and the temperature.Various models have been proposed to simulate the wear of the cutter.For example, U.S. Pat. No. 6,619,411 issued to Singh et al. (the '411patent) discloses methods for modeling the wear of a roller cone drillbit.

As disclosed in the '411 patent, abrasion of materials from a drill bitmay be analogized to a machining operation. The volume of wear producedwill be a function of the force exerted on a selected area of the drillbit and the relative velocity of sliding between the abrasive materialand the drill bit. Thus, in a simplistic model,WR=f(F _(N) ,v),  (6)where WR is the wear rate, F_(N) is the force normal to the area on thedrill bit and v is the relative sliding velocity. F_(N), which is afunction of the bit-formation interaction, and v can both be determinedfrom the above-described simulation.

While the simple wear model described above may be sufficient for wearsimulation, other embodiments of the invention may use any othersuitable models. For example, some embodiments of the invention use amodel that takes into account the temperature of the operation, such as:WR=f(F _(N) ,v,T),  (7)while other embodiments may use a model that includes anothermeasurement as a substitute for the force acting on the bit or cutter.For example, the force acting on a cutter may be represented as afunction of the depth of cut (d). Therefore, F_(N) may be replace by thedepth of cut (d) in some model, as shown in equation (8):WR=a1×10^(a2) ×d ^(a5) ×v ^(a4) ×T ^(a5)  (8)where WR is the wear rate, d is the depth of cut, v is the relativesliding velocity, T is a temperature, and a1-a5 are constants.

The wear model shown in equation (8) is flexible and can be used tomodel various bit-formation combinations. For each bit-formationcombination, the constants (a1-a5) may be fine tuned to provide anaccurate result. These constants may be empirically determined usingdefined formations and selected bits in a laboratory or from dataobtained in the fields. Alternatively, these constants may be based ontheoretical or semi-empirical data.

The term a1×10^(a2) is dependent on the bit/cutter (material, shape,arrangement of the cutter on the bit, etc.) and the formationproperties, but is independent of the drilling parameters. Thus, theconstants a1 and a2 once determined can be used with similarbit-formation combinations. One of ordinary skill in the art wouldappreciate that this term (a1×10^(a2)) may also be represented as asimple constant k.

The wear properties of different materials may be determined usingstandard wear tests, such as the American Society for Testing andMaterials (ASTM) standards G65 and B611, which are typically used totest abrasion resistance of various drill bit materials, including, forexample, materials used to form the bit body and cutting elements.Further, superhard materials and hardfacing materials that may beapplied to selected surfaces of the drill bit may also be tested usingthe ASTM guidelines. The results of the tests are used to form adatabase of rate of wear values that may be correlated with specificmaterials of both the drill bit and the formation drilled, stresslevels, and other wear parameters.

The remaining term in equation (8), d^(a3)×v^(a4)×T^(a5) is dependent onthe drilling parameters (i.e., the depth of cut, the relative slidingvelocity, and the temperature). With a selected bit-formationcombination, each of the constants (a3, a4, and a5) may be determined byvarying one drilling parameter and holding other drilling parametersconstant, For example, by holding the relative sliding velocity (v) andtemperature (T) constant, a3 can be determined from the wear ratechanges as a function of the depth of cut (d). Once these constants aredetermined, they can be used in the dynamic simulation and may also bestored in a database for later simulation/modeling.

The performance of the worn cutters may be simulated with a constrainedcenterline model or a dynamic model to generate parameters for the worncutters and a graphical display of the wear. The parameters of the worncutters can be used in a next iteration of simulation. For example, theworn cutters can be displayed to the design engineer and the parameterscan be adjusted by the design engineer accordingly, to change wear or tochange one or more other performance characteristics. Simulating,displaying and adjusting of the worn cutters can be repeated, tooptimize a wear characteristic, or to optimize or one or more otherperformance characteristics. By using the worn cutters in thesimulation, the results will be more accurate. By taking into accountall these interactions, the simulation of the present invention canprovide a more realistic picture of the performance of the drill bit.

Note that the simulation of the wear may be performed dynamically withthe drill bit attached to a drill string. The drill string may furtherinclude other components commonly found in a bottom-hole assembly (BHA).For example, various sensors may be included in drill collars in theBHA. In addition, the drill string may include stabilizers that reducethe wobbling of the BHA or drill bit.

The dynamic modeling may also take into account the drill stringdynamics. In a drilling operation, the drill string may swirl, vibrate,and/or hit the wall of the borehole. The drill string may be simulatedas multiple sections of pipes. Each section may be treated as a “node,”having different physical properties (e.g., mass, diameter, flexibility,stretchability, etc.). Each section may have a different length. Forexample, the sections proximate to the BRA may have shorter lengths suchthat more “nodes” are simulated close to BHA, while sections close tothe surface may be simulated as longer nodes to minimize thecomputational demand.

In addition, the “dynamic modeling” may also take into account thehydraulic pressure from the mud column having a specific weight. Suchhydraulic pressure acts as a “confining pressure” on the formation beingdrilled. In addition, the hydraulic pressure (i.e., the mud column)provides buoyancy to the BHA and the drill bit.

The dynamic simulation may also generate worn cutters after eachiteration and may use the worn cutters in the next iteration. By usingthe worn cutters in the simulation, the results will be more accurate.By taking into account all these interactions, the dynamic simulation ofthe present invention can provide a more realistic picture of theperformance of the drill bit.

Returning to FIG. 5B, once interactions of all of the cutting elementson a blade is determined, blade interaction with the formation may bedetermined by checking the node displacements at the blade surface, at262, to determine if any of the blade nodes are out of bounds or makecontact with the wellbore wall or bottomhole surface. If blade contactis determined to occur during the incremental rotation, the contact areaand depth of penetration of the blade are calculated and used todetermine corresponding interaction forces on the blade surfaceresulting from the contact. Once forces resulting from blade contactwith the formation are determined, or it is determined that no bladecontact has occurred, the total interaction forces on the blade duringthe incremental rotation are calculated by summing all of the cuttingelement forces and any blade surface forces on the blade, at 268.

Once the interaction forces on each blade are determined, any forcesresulting from contact of the bit body with the formation may also bedetermined and then the total forces acting on the bit during theincremental rotation calculated and used to determine the dynamic weighton bit 278. The newly calculated bit interaction forces are then used toupdate the global load vector at 279, and the response of the drillingtool assembly is recalculated at 280 under the updated loadingcondition. The newly calculated response is then compared to theprevious response at 282 to determine if the responses are substantiallysimilar. If the responses are determined to be substantially similar,then the newly calculated response is considered to have converged to acorrect solution. However, if the responses are not determined to besubstantially similar, then the bit interaction forces are recalculatedbased on the latest response at 284 and the global load vector is againupdated at 284. Then, a new response is calculated by repeating theentire response calculation (including the wellbore wall constraintupdate and drill bit interaction force update) until consecutiveresponses are obtained which are determined to be substantially similar(indicated by loop 285), thereby indicating convergence to the solutionfor dynamic response to the incremental rotation.

Once the dynamic response of the drilling tool assembly to anincremental rotation is obtained from the response force update loop285, the bottomhole surface geometry is then permanently updated at 286to reflect the removal of formation corresponding to the solution. Atthis point, output information desired from the incremental simulationstep can be stored and/or provided as output. For example, the velocity,acceleration, position, forces, bending moments, torque, of any node inthe drill string may be provided as output from the simulation.Additionally, the dynamic WOB, cutting element forces, resulting cutterwear, blade forces, and blade or bit body contact points may be outputfrom the simulation.

This dynamic response simulation loop 240 as described above is thenrepeated for successive incremental rotations of the bit until an endcondition of the simulation (checked at 290) is satisfied. For example,using the total number of bit revolutions to be simulated as thetermination command, the incremental rotation of the drilling toolassembly and subsequent iterative calculations of the dynamic responsesimulation loop 240 will be repeated until the selected total number ofrevolutions to be simulated is reached. Repeating the dynamic responsesimulation loop 240 as described above will result in simulating theperformance of an entire drilling tool assembly drilling earthformations with continuous updates of the bottomhole pattern as drilled,thereby simulating the drilling of the drilling tool assembly in theselected earth formation. Upon completion of a selected number ofoperations of the dynamic response simulation loop, results of thesimulation may be used to generate output information at 294characterizing the performance of the drilling tool assembly drillingthe selected earth formation under the selected drilling conditions, asshown in FIG. 5A-C. It should be understood that the simulation can bestopped using any other suitable termination indicator, such as aselected wellbore depth desired to be drilled, indicated divergence of asolution, etc.

The dynamic model of the drilling tool assembly described above usefullyallows for six degrees of freedom of moment for the drill bit. In one ormore embodiments, methods in accordance with the above description canbe used to calculate and accurately predict the axial, lateral, andtorsional vibrations of drill strings when drilling through earthformation, as well as bit whirl, bending stresses, and other dynamicindicators of performance for components of a drilling tool assembly.

Optimizing Performance for a Dynamic Model

In another aspect, the invention provides a method for predicting,analyzing, improving and optimizing the performance of a drilling toolassembly and particularly the performance of a drill bit design when itis drilling in earth formations. For example, the method may includesimulating a dynamic response of a drilling tool assembly, determiningthe radial components and circumferential components of the totalimbalanced force, determining the Beta angle between the componentforces over a period of time, determining the bottom hole pattern,determining the dynamic trajectory of the centerline of the drill bit,and/or determining the side rake imbalance forces, displaying at leastone of the determined performance indicating, adjusting the value of atleast one drill bit design parameter including the side rake angledistribution, repeating the simulating, and repeating the adjusting andthe simulating until a value of at least one performance indicatingparameter is determined to be an optimal value.

Methods in accordance with this aspect of the invention may be used toanalyze relationships between drill bit design parameters and theperformance indicating parameters such as the radial components andcircumferential components of the total imbalanced force, the Beta anglebetween the component forces over a period of time, the bottom holepattern, the dynamic trajectory of the centerline of the drill bitand/or the side rake imbalance forces and the relationship of thesecharacteristics of the drill bit design and performance to other designparameters and performance characteristics. This method also may be usedto design a drilling tool assembly having enhanced drillingcharacteristics. Further, the method may be used to analyze the effectof changes in a drilling tool configuration on drilling performance.Additionally, the method may enable a drilling tool assembly designer oroperator to determine an optimal value of a drill bit design parameteror of a drilling tool assembly design parameter for drilling at aparticular depth or in a particular formation.

Examples of drilling tool assembly design parameters include the typeand number of components included in the drilling tool assembly; thelength, ID, OD, weight and material properties of each component; andthe type, size, weight, configuration, and material properties of thedrill bit; and the type, size, number, location, orientation, andmaterial properties of the cutting elements on the bit, and in oneparticular embodiment, the side rake angle distribution. Materialproperties in designing a drilling tool assembly may include, forexample, the strength, elasticity, density, wear resistance, hardness,and toughness of the material. It should be understood that drillingtool assembly design parameters may include in addition to the side rakeangle distribution any other configuration of parameter for the drillingtool assembly without departing from the spirit of the invention.

Examples of drilling performance parameters include rate of penetration(ROP), rotary torque required to turn the drilling tool assembly, rotaryspeed at which the drilling tool assembly is turned, drilling toolassembly vibrations induced during drilling (e.g., lateral and axialvibrations), weight on bit (WOB), and forces acting on the bit, cuttingsupport structure, and cutting elements. Drilling performance parametersmay also include the inclination angle and azimuth direction of theborehole being drilled. One skilled in the art will appreciate thatother drilling performance parameters exist and may be considered asdetermined by the drilling tool assembly designer without departing fromthe scope of the invention.

In one embodiment of the invention, illustrated in FIG. 6, the methodcomprises defining, selecting or otherwise providing initial inputparameters at 300 (including drill bit and drilling tool assembly designparameters). The method may further comprise simulating the response ofa drill bit design using a static model 302 (a static model defined forthese purposes as a model in which it is assumed that the centerline ofthe drill bit is constrained to be concentric with the centerline of thewellbore while the drill bit is rotated through increments of simulatedrotational drilling in an earth formation) to determine cutter wear data304. The method further comprises using the wear data in a dynamic model(defined as a model in which the centerline of the drill bit isconstrained only by the dynamic characteristics of the drilling toolassembly including the drill string and the drill bit design) andsimulating the dynamic response of the drilling tool assembly at 310.The dynamic simulation may be used to determine a radial component 312and a circumferential component 314 of the total imbalanced forces (TIF)on the drill bit and the Beta angle 318 between the radial andcircumferential vector components 312 and 314. The total imbalance forcevector TIF may be determined and/or minimized. Other performanceindicating parameters may also be determined. For example, thebottomhole pattern may be determined at 322, the centerline trajectorymay be determined at 324 and/or the side rake imbalance force vector(SRIF) may be determined at 326. The method further comprises adjustingat least one drilling tool assembly design parameter including the siderake angle distribution at 328 in response to one or more of thedetermined performance parameters, and repeating the simulating of thedrilling tool assembly 330. The method also comprises evaluating thechange in value of at least one of the performance parameters, and basedon that evaluation, repeating the adjusting, the simulating, and theevaluating until at least one performance parameter is optimized.

In one embodiment the total imbalance forces may be determined and/ordecreased at 316 to an acceptably small force and even minimized priorto, or concurrently with, the process for modifying or optimizing theperformance parameters for the simulated drilling.

As used herein “optimized” or “optimizing” means obtaining animprovement in a particular characteristic that is acceptable to thedesigner for the intended purposes of the drill bit design. This may forexample satisfy criterion set by the bit designer for a design providingan acceptable value for a particular performance parameter or acceptablevalues for a selected group of performance parameters as determined bymodeling, laboratory testing, field testing or field use to produce aconsistently stable drill bit in a given type or a given variety oftypes of formations and for intended operating parameters. This may forexample satisfy criterion set by the designer for a design providing asooth bottom hole pattern, a small TIF, a small SRIF, a small diametertrajectory, or a Beta angle at 180 degrees for a sufficient portion ofthe time or for a larger percent of the time as determined by modeling,testing, or field use to produce a consistently stable drill bit in agiven type or a given variety of types of formations and for intendedoperating parameters.

In the case of a constrained centerline model, the graphical depictioncan include dynamic movement in the axial direction while the fixedcutter drill bit is constrained about the centerline of the wellbore,but the bit is only allowed to move up and down and rotate around thewell axis. Based upon the teachings of the present invention, it will beappreciated that other embodiments may be derived with or without thisconstraint. For example, a fully dynamic model of the fixed cutter drillbit allows for six degrees of freedom for the drill bit. Thus, using adynamic model in accordance with embodiments of the invention allows forthe prediction of axial, lateral, and torsional vibrations as well asbending moments at any point on the drill bit or along a drilling toolassembly as may be modeled in connection with designing the drill bit.

In the embodiment of FIG. 7, initial parameters 400 may include initialdrilling tool assembly parameters 402, initial drilling environmentparameters 404, drilling operating parameters 406, and drilling toolassembly/drilling environment interaction parameters and/or models 408.These parameters may be substantially the same as the input parametersdescribed above for the previous aspect of the invention.

In this example, simulating 411 comprises constructing a mechanicsanalysis model of the drilling tool assembly 412 based on the drillingtool assembly parameters 402, determining system constraints at 414using the drilling environment parameters 404, and then using themechanics analysis model along with the system constraints to solve forthe initial static state of the drilling tool assembly in the drillingenvironment 416. Simulating 411 further comprises using the mechanicsanalysis model along with the constraints and drilling operationparameters 406 to incrementally solve for the response of the drillingtool assembly to rotational input from a rotary table 418 and/ordownhole motor, if used. In solving for the dynamic response, theresponse is obtained for successive incremental rotations until an endcondition signaling the end of the simulation is detected.

Incrementally solving for the response may also include determining,from drilling tool assembly/environment interaction information, loadson the drilling tool assembly during the incremental rotation resultingfrom changes in interaction between the drilling tool assembly and thedrilling environment during the incremental rotation, and thenrecalculating the response of the drilling tool assembly under the newconstraint loads. Incrementally solving may further include repeating,if necessary, the determining loads and the recalculating of theresponse until a solution convergence criterion is satisfied.

In the example shown in FIG. 7, adjusting at least one drilling toolassembly design parameter 426 comprises changing a value of at least onedrilling tool assembly design parameter after each simulation by datainput from a file, data input from an operator, or based on calculatedadjustment factors in a simulation program. For example, the side rakeangle distribution may be adjusted.

Drilling tool assembly design parameters may include any number of thedrilling tool assembly parameters in addition to modifications to theside rake angle distribution. Thus in one example, a design parameter,such as the length of a drill collar, can be repeatedly adjusted andsimulated to determine the effects of BHA weight and length on adrilling performance parameter (e.g., ROP, TIF, SRIF, Beta angle, bottomhole pattern, and/or centerline trajectory). Similarly, the innerdiameter or outer diameter of a drilling collar may be repeatedlyadjusted and a corresponding change response obtained. Similarly, astabilizer or other component can be added to the BHA or deleted fromthe BHA and a corresponding change in response obtained. Further, adrill bit design parameter may be repeatedly adjusted and correspondingdynamic responses obtained to determine the effect on a performanceparameter of changing one or more drill bit design parameters, such asthe cutting support structure profile (e.g., cutter layout, bladeprofile, cutting element shape and size, orientation and/or back rakeangle distribution) on the drilling performance of the drilling toolassembly.

In the example of FIG. 7, repeating the simulating 411 for the“adjusted” drilling tool assembly comprises constructing a new (oradjusted) mechanics analysis model (at 412) for the adjusted drillingtool assembly, determining new system constraints (at 414), and thenusing the adjusted mechanics analysis model along with the correspondingsystem constraints to solve for the initial static state (at 416) of theof the adjusted drilling tool assembly in the drilling environment.Repeating the simulating 411 further comprises using the mechanicsanalysis model, initial conditions, and constraints to incrementallysolve for the response of the adjusted drilling tool assembly tosimulated rotational input from a rotary table and/or a downhole motor,if used.

Once the response of the previous assembly design and the response ofthe current assembly design are obtained, the effect of the change invalue of at least one design parameter on a performance indicatingparameter can be evaluated (at 422). For example, during eachsimulation, values of desired drilling performance parameters (ROP, TIF,SRIF, Beta angle, bottomhole pattern, centerline trajectory, impactloads, axial, lateral, or torsional vibration, and etc.) can becalculated and stored. Then, these values or other factors related tothe drilling response, can be analyzed to determine the effect ofadjusting the drilling tool assembly design parameter on the value ofthe at least one drilling performance parameter.

Once an evaluation of at least one drilling parameter is made, based onthat evaluation the adjusting and the simulating may be repeated untilit is determined that the at least one performance parameter isoptimized or an end condition for optimization has been reached (at424). The performance parameter may be determined to be at an optimalvalue when the performance parameter is at or near a predetermined valuefor the simulated drilling. It has been found that such an optimizationof the dynamic model provides improved drilling stability and thusminimized axial or lateral impact force or evenly distributed forcesabout the cutting structure of a drill bit. For example, an increasedaverage Beta angle over a period of dynamically modeled drillingsimulation can indicate optimized stability of the drill bit and canalso be an indicator of other performance parameters such as a maximumrate of penetration, a minimum rotary torque for a given rotation speed,and/or most even weight on bit for a given set of adjustment variables.

Usefully, embodiments of the invention may be used to analyze therelationship between drilling tool assembly design parameters anddrilling performance in a selected drilling environment. Additionally,embodiments of the invention may be used to design a drilling toolassembly having optimal drilling performance for a given set of drillingconditions. Those skilled in the art will appreciate that otherembodiments of the invention exist which do not depart from the spiritof this aspect of the invention.

Examples of Side Rake Angle Distribution Adjustments

FIG. 11 shows a partial end view of a fixed cutter bit 500 with atypical distribution of side rake angles along one exemplary blade 501,in which the side rake angle distribution is not optimum. A plurality ofindividual cutters 502-511 are positioned having side rake angles512-521 respectively. The side rake angles 512-521 are determined bymeasuring the angle α_(sr) between an imaginary line 522 drawn throughthe center and perpendicular to a cutting face of a cutter and a tangentline 523 at the center of the cutter. Thus, the tangent line 523 isparallel to the direction of cutting for the cutter when the drill bitis rotated about the center 524 of the drill bit. In FIG. 11, thecutters 502-506 are in the cone region 525, the cutters 507-510 are inthe nose region 526, and cutter 511 are in the shoulder or gauge region527 of the drill bit 500. The side rake angle distribution in each ofthe regions 525, 526, and 527 are considered generally “flat” as all ofthe cutters 502-511 have essentially the same side rake angle of aboutzero degrees (α_(sr)=0.0°).

FIG. 12 shows a partial end view of a fixed cutter bit 530 with amodified distribution of side rake angles along one exemplary blade 531and in which the modified side rake angle distribution improvesperformance over the side rake angle distribution shown in FIG. 11. Aplurality of individual cutters 532-541 are positioned having side rakeangle 542-551 respectively. The side rake angles 542-551 are determinedby measuring the angle α_(sr) between an imaginary line 552 drawnthrough the center and perpendicular to a cutting face of a cutter and atangent line 553 at the center of the cutter. Thus, the tangent line 553is parallel to the direction of cutting for the cutter when the drillbit is rotated about its center 554. In FIG. 12, the cutters 532-536 arein the cone region 555, the cutters 537-540 are in the nose region 556,and cutter 541 is in the shoulder or gauge region 557 of the drill bit530. The side rake angle distribution in the cone region 555 varies froma large side rake angle toward the center 554 of the drill bit 530 andprogressively smaller side rake angles in the cone region 555 toward thenose region 556, smaller in the nose region and then smaller yet towardthe shoulder or gauge region 557. For example, from a large side rakeangle 542 of about eleven degrees (11°) at the cutter 532, to a siderake angle 543 of about ten degrees (10°) at cutter 533, to a side rakeangle 544 of about nine degrees (9°) at cutter 534, to a side rake angle545 of about eight degrees (8°) at cutter 535, a side rake angle 546 ofabout seven degrees (7°) at cutter 536, and a side rake angle 547 ofabout six degrees (6°) at cutter 537 in the cone region 555. In the noseregion, the distribution may, for example, include a side rake angle 548of about five degrees (5°) at cutter 538 and a side rake angle 549 ofabout four degrees (4°) at cutter 539. In the shoulder and gauge region,a side rake angle 551 of about three degrees (3°) might be provided atcutter 541 and others if any along the gauge (not shown). It will beunderstood that the side rake angles 542-551 and the distributionprovided by the combination of side rake angles indicated for thecutters 532-541 of FIG. 12 are examples only and that other side rakeangles and other side rake angle distributions may be provided with outdeparting from the scope of the invention.

FIG. 13 shows a schematic end view of a drill bit 560 having a layout ofa plurality of fixed cutters (601, 603, 605, 610, 615, 620, 625 and 630)on a lead blade 561, a plurality of cutters (606, 611, 616, 621, 626 and631) on a trailing blade 562. A plurality of cutters is also depicted onanother lead blade 563 and on additional trailing blades 564 and 565. Animaginary circle 566 is generally at the nose 567 and indicates that thecone region 568 is inside of the circle 566. Outside of the circle 566the nose region 567 joins with the shoulder 569 and the gauge 570. Ithas been found by the inventors that by modifying the various side rakeangles of the cutters in the cone area, the nose area, and/or theshoulder area the performance of the drill bit can be improved.Indications of improved performance include a smaller dynamic centerlinetrajectory for the drill bit and corresponding improved stability of thedrill bit when drilling in a formation. Table 1 below shows a variety ofside rake angle distributions for cutters located on a drill bit invarious areas or regions. An outward side rake angle (i.e., with theface of the cutter tilted outward from a tangent line) is considered apositive side rake angle and an inward side rake angle is designatedwith a negative number.

TABLE 1 Side Rake Angle Distribution (Degrees) Inside Outside #1 cutterInner cutters of Nose Nose Cutters of Nose Shoulder 0.0-5.0  4.0-5.0 4.0-3.0  3.0-2.0  3.0-1.0  2.0-0.0  0.0-15.0 1.0-15.0 1.0-15.0 1.0-15.01.0-15.0 1.0-15.0 12.0 10.0 8.0 5.0 5.0 3.0 5.0 4.0 −1.0 −2.0 −3.0 −2.05.0 5.0 4.0 2.0 −2.0 −2.0

The description above generally describes side rake angle distributionsof cutters on the same blade. Some embodiments of the invention haveside rake angle distributions coordinated among cutters on differentblades. FIG. 14 shows a schematic layout of the cutter alignments whenall the blades are superimposed. The profile is one that might begenerated across one radial plane by the rotation of the fixed cutterson the drill bit 560 of FIG. 13. As shown in FIG. 14, the side rakeangle distribution of the cutters exhibits a gradual change, or“blending,” of the side rake angles from the most inward cutter 601 tothe most outward cutter 634. In this embodiment the cutters 601-634effectively define a cutter profile shape including a cone region 641, anose region 642, a shoulder region 643 and a gauge region 645. Theimproved side rake angle distribution includes blending in the conesection 641 of the side rake angle from five degrees (5°) side rakeangle for the first cutter 601 adjacent to the central axis 640 of thecone 641 and progressively decreasing side rake angle in cutters 602-610down to one degree (1.0°) at the nose region 642 (cutters 611-616), andfurther decreasing down to zero degrees (0.0°) around the shoulderregion 643 and gauge region 645 of the drill bit 560. Thus the gradualchange of side rake angles among the cutters is coordinated among allthe blades of the drill bit 560.

FIG. 15 shows a partial schematic end view layout of some of the cuttersof the drill bit 560 of FIGS. 13 and 14. The cutters 601, 603, 605, and610 are shown on a first leading blade, while cutters 602, 604, and 609are on a leading second blade. In this embodiment the side rake anglefor the cutter 602 on the second blade will be between the side rakeangles for cutters 601 and 603 on the first leading blade. Similarly theside rake angle for the cutter 604 on the second leading blade will bebetween the side rake angles for cutters 603 and 605 on the firstleading blade. For example, the cutters 601, 603, 605, and 610 have amodified side rake angle distribution of five, four, three, and twodegrees (5.0°, 4.0°, 3.0°, and 2.0°) respectively, and the cutters 602and 604 have a modified side rake angle distribution of four andone-half, and three and one-half degrees (4.5°, and 3.5°) respectively.

In other embodiments, the cutters can include higher side rake angles. Ahigher side rake angle can reduce the frontal impact to the cutter,reduce torque fluctuations, and may allow for more aggressive cuttergeometries by reducing the cross section of earthen material in front ofa cutter, reducing the fracture plane extending across the ridge beingcut. The higher side rake can reduce the cut force on the face of thecutter and smooth the torque fluctuations produced by the drill bit.Additionally, higher side rake angles can present a sharper cutting edgeto the formation and can lead to a higher ROP. In some embodiments, siderake angles can be greater than about 15 degrees; in other embodiments,side rake angles can be up to about 45 degrees or more. In someembodiments, a side rake angle of a cutter can be substantially up toabout 90 degrees.

Referring again to FIG. 14, in some embodiments, a cutter in a coneregion 641 may have a side rake angle greater than about 15 degrees andless than about 90 degrees, and a cutter in a nose region 642 may have aside rake angle smaller than the side rake angle of the cutter in thecone region 641. In other embodiments, the cutters along the cone region641 of the blade of the fixed cutter drill bit may have a side rakeangle distribution including a cutter in the cone region 641 toward thecenter of drill bit having a side rake angle in a range of greater than15 degrees and up to about 45 degrees, the cutters in the nose region642 may have side rake angles in a range of about −3 degrees to about 40degrees, and the side rake angles of cutters in the cone region 641between the cutters toward the center and the cutters at the nose region642 may be blended, as described above.

Referring again to FIG. 15, in some embodiments the cutters may includeside rake angles of greater than 15 degrees. For example, the cutters601, 603, 605, and 610 may have a modified side rake angle distributionof 45, 43, 41, and 39 degrees (45.0°, 43.0°, 41.0°, and 39.0°)respectively, and the cutters 602 and 604 may have a modified side rakeangle distribution of 44 and 42 degrees (44.0°, and 42.0°) respectively,with side rake angles progressively decreasing through the nose,shoulder, and gauge regions.

Displaying Performance Parameters Affected by Modified Side Rake AngleDistribution

As noted above, output information from a dynamic simulation of adrilling tool assembly drilling an earth formation may include, forexample, the drilling tool assembly configuration (or response) obtainedfor each time increment, and corresponding cutting element forces, bladeforces, bit forces, impact forces, friction forces, dynamic WOB, bendingmoments, displacements, vibration, resulting bottomhole geometry, radialand circumferential components of total imbalance forces, Beta anglebetween the components of the imbalance forces, side rake imbalanceforces, centerline trajectory, and more. Among these, vibration, totalimbalance force (TIF), Beta angle, bottom hole pattern, centerlinetrajectory and side rake imbalance force (SRIF) are considered sensitiveto side rake angle distribution. Therefore these parameters can provideuseful indication for side rake angle optimization. However, based uponthe present disclosure, one of ordinary skill will appreciate that anyoutput parameter sensitive to side rake angle changes may be used tomonitor the side rake angle distribution optimization process. Thisoutput information may be presented in the form of a visualrepresentation (indicated at 294 in FIG. 5C).

Examples of the visual representations include a visual representationof the dynamic output information for the drilling tool assemblypresented on a computer screen. Usefully, the visual representation mayinclude a historic representation of the output information over a givenperiod of time or a given number of rotations that are calculated orotherwise obtained during the simulation. For example, a time history ofthe dynamic total imbalance forces, the Beta angle, the side rakeimbalance forces, and the centerline trajectory over a period of time ora number of rotations during simulated drilling may be graphicallydisplayed to a designer. The means used for visually displaying theoutput information simulated during drilling is a matter of conveniencefor the system designer, and not a limitation on the invention.

FIG. 16 shows a graphical depiction of various imbalance forces. Asshown a plurality of cutters 906 are spatially oriented on a drill bit908 with cutting forces 910 and radial forces 912 on each cutter. Thedisplay can be presented at increments of rotation. A sequence orrotation increments can also be displayed. As the bit 908 issequentially rotated according to the simulation, the cutting forces 910and the radial forces 912 on each of the individual cutters 906 willchange according to the forces determined at each increment of rotation.A graphically displayed plot 914 of a selected force, for example thetotal imbalance force (TIF) 922, may be displayed relative to thesimulated drilling depth. The components of the total imbalance force(TIF) 922 acting on the center of on the drill bit are depictedincluding a circumferential imbalance force vectors (CIF) 918 calculatedas the vector sum of all the individual cutting forces 910, and a radialimbalance force vector (RIF) 920 calculated as the vector sum of all theindividual radial forces 912 for all of the cutters 906 on the drill bit908. A visual depiction of the Beta angle 924 between the totalimbalance force components (CIF) 918 and (RIF) 920 is also graphicallydisplayed. Similar to the computation for the CIF and the RIF, theimbalance force due to the side fake of each cutter can be computed andcombined to give and to display the side rake imbalance force (SRIF) 923for the drill bit. The side rake angle distribution may be optimized, toreduce the SRIF or one or more of the various other imbalance forces.Alternatively, one or more of the imbalance forces may be otherwisereduced to an extent possible without changing the side rake angledistribution and then the side rake angle distribution may be optimizedto further reduce the same or another one of the one or more imbalanceforces. Similarly, the side rake angle distribution may be optimized, toproduce a Beta angle at or near 180 degrees for a larger portion of thetime. Alternatively, the Beta angle at or near 180 degrees for a largeportion of the time may be optimized to an extent possible withoutchanging the side rake angle distribution and then the side rake angledistribution may be optimized to further increase the portion of thetime that the Beta angle is at or near 180 degrees.

FIG. 17 shows a graphical display of a group of worn cutters 930 for asingle blade of a drill bit, illustrating different extents of wear, forexample, at 931, 932, 933, 934, and 935 on the cutters 930 in accordancewith an embodiment of the invention. Being able to model the wear of thecutting elements (cutters) and/or the bit accurately makes it possibleto design a fixed cutter bit to achieve the desired wearcharacteristics. In addition, it has been found that the demand ofcomputing power and speed can be reduced by using wear modelingconducted in a static or constrained centerline model and then insertingthe wear data into a dynamic model at the appropriate times for useduring a dynamic drilling modeling to update the drill bit parametersaccording to the simulated wear predicted with the simpler static wearmodel. Inventors have found that this can significantly improve thespeed of the dynamic modeling computations without significantlyreducing the accuracy of the drilling simulation because the wear ratesand results are similar for both constrained centerline analysis and fordynamic analysis.

Graphically Displaying Results of Modeling and Simulation

According to one aspect of the invention output, information from themodeling may be presented in the form of a visual representation.

Other exemplary embodiments of the invention include graphicallydisplaying results of the modeling or simulation of the performance ofthe fixed cutter drill bit, the performance of the cutters, orperformance characteristics of the fixed cutter drill bit drilling in anearth formation. Graphically displaying the drilling performance may befurther enhanced by also displaying input parameters.

FIG. 18 shows an example of modeling and of graphically displayingperformance of individual cutters 930 of a fixed cutter drill bit, forexample cut area shape and distribution, together with performancecharacteristics of the drill bit, for example total imbalance force 922,and Beta angle 924 between the circumferential and radial components 918and 920, respectively, in accordance with an embodiment of the presentinvention.

According to one alternative embodiment, FIG. 18 also shows an exampleof modeling and of graphically displaying performance of individualcutters of a fixed cutter drill bit, for example cut area shapes 936,938, 940, and 942 and distribution of loading represented by a colorcoding, shown here as a the gray scale, at 944, together withperformance characteristics of the drill bit and in particularcomponents of a total imbalance force vector (TIF) at 922, includingradial imbalance force vector component (RIF) at 920 and thecircumferential imbalance force vector component (CIF) at 918 of thetotal imbalance force. The Beta angle 924 between the forces componentsapplied to the center of the drill bit is also depicted. In accordancewith one embodiment the Beta angle 924 is presented as a performanceparameter that can be visually observed by the design engineer to get afeel for the effect of any adjustments made to the drill bit designparameters (e.g., side rake angle distributions). The magnitude of theforces and the directions are visually displayed. The components ofimbalance forces and the components of the forces may also be displayedin a time sequence depiction to help visualize the duration of the Betaangle remaining at or above a given level for a portion of the simulateddrilling time. The design engineer can select any portion of thepossible information to be provided visually in such graphical displays.For example, an individual cutter can be selected; it can be virtuallyrotated and studied from different orientations. The design parameters(e.g., side rake angles) of individual cutters can be adjusted and thesimulation repeated to provide another graphical display. The adjustmentcan be made to change the performance characteristics. The adjustmentscan also be made, repeatedly if necessary, to optimize a parameter or aplurality of parameters of the design for an optimum resultant Betaangle and duration of the Beta angle at or near 180 degrees.

FIG. 19 shows a bottom hole cutting pattern 700 simulated with a drillbit, in which the side rake angle distribution is not optimum, as forexample the drill bit depicted in FIG. 11 above. It is observed thatover a period of simulated drill bit revolutions the bottom hole pattern700 has chatter marks 702 along the various cut paths 704 made by theseries of cutters 706. The rough cutting pattern can indicateinstability of the drill bit and a decreased rate of penetration. Thesmoothness and uniformity of the bottom hole pattern is not optimizedand thus the side rake angle distribution that produced this simulatedbottom hole pattern is not optimum.

FIG. 20 shows a bottom hole cutting pattern 710 simulated with a drillbit, in which the side rake angle distribution according to oneembodiment of the invention, as for example one of the side rake angledistributions shown in FIGS. 12, 13, 14, 15, or in Table 1 above. It isobserved that over a period of simulated drill bit revolutions thebottomhole pattern 710 has smooth, uniform, concentric circulartrough-shaped cutting paths 712 made by the series of cutters 716. Thesmooth, uniform cutting pattern 710 can indicate stability of the drillbit and an increased rate of penetration. The smoothness and uniformityof the bottom hole pattern might be considered optimized such that aside rake distribution might be considered optimized based uponobservation of this performance parameter.

FIG. 21 shows a historic graphical plot of side rake imbalance forces(SRIF) simulated with a drill bit having a typical side rake angledistribution, as for example the side rake distribution depicted in FIG.11 above. The SRIF may be computed in a similar manner to thecalculations of CIF and RIF (circumferential and radial components ofimbalance force). Each cutter has an effective side rake because of thecut shape imposed on the cuter by the bottom hole geometry created bycut path overlap. This means that even if a cutter is assembled on theprofile and is defined to have 0.0 degrees side rake at the assembly tippoint, the cutter may generate some side cutting force because of theinterference pattern generated. Thus for each cutter, the side force canbe computed at 0.0 degrees side rake or at any other side rake angle setfor individual cutters and then the vector total for all the cutters canbe calculated to give the SRIF for the drill bit. It is observed thatover a period of simulated drill bit revolutions, the SRIF variessignificantly and has cyclically high values that can indicateinstability of the drill bit. The performance parameter SRIF is notoptimized and thus the side rake angle distribution of this drill bit isnot optimum.

FIG. 22 shows a historic graphical plot of side rake imbalance forces(SRIF) simulated with a drill bit having an improved side rake angledistribution according to one embodiment of the invention, as forexample one of the side rake angle distributions shown in FIGS. 12, 13,14, 15, or in Table 1 above. It is noted that the SRIF stabilize after afew simulated revolutions of the drill bit to a consistent andrelatively low values. Such a side rake angle distribution might beconsidered optimized based upon observation of this performanceparameter.

FIG. 23 shows a centerline trajectory pattern simulated with a drill bithaving a typical side rake angle distribution that is not optimum, asfor example the side rake distribution depicted in FIG. 11 above. It isobserved that over a period of simulated drill bit revolutions, thecenterline trajectory varies significantly and the trajectory patternhas relatively large diameter that can indicate side impact with thebore hole, alternating imbalance forces and instability of the drillbit. The centerline trajectory as a performance parameter is notoptimized and thus the side rake angle distribution that produces such atrajectory is not optimum.

FIG. 24 shows a centerline trajectory pattern simulated with a drill bithaving an improved side rake angle distribution according to oneembodiment of the invention as for example one of the side rake angledistributions shown in FIGS. 12, 13, 14, 15, or in Table 1 above. It isnoted that over a period of simulated drill bit revolutions, thecenterline trajectory does not vary significantly and the trajectorypattern has a relatively small total diameter that can indicatestability of the drill bit. The centerline trajectory as a performanceparameter could be considered as optimized and thus the side rake angledistribution that produces such a trajectory might be consideredoptimized based upon observation of this performance parameter.

FIG. 25 shows a historic graphical plot of total imbalance forces (TIF)simulated with a drill bit having a typical side rake angle distributionthat is not optimum, as for example the side rake distribution depictedin FIG. 11 above. It is observed that over a period of simulated drillbit revolutions the TIF vary significantly and have cyclically highvalues that can indicate instability of the drill bit. The performanceparameter TIF is not optimized and thus the side rake angle distributionthat produces such a TIF plot is not optimum.

FIG. 26 shows a historic graphical plot of TIF simulated with a drillbit having an improved side rake angle distribution according to oneembodiment of the invention, as for example one of the side rake angledistributions shown in FIGS. 12, 13, 14, 15, or in Table 1 above. It isnoted that the TIF are minimized during many of the simulatedrevolutions of the drill bit, the peak TIF are relatively low and thereare relatively few peaks. Such a side rake angle distribution might beconsidered optimized based upon observation of this performanceparameter.

FIG. 27 shows a historic graphical plot of Beta angles between thecircumferential and the radial components of the total imbalance forcessimulated with a drill bit having a typical side rake angle distributionthat is not optimum, as for example the side rake distribution depictedin FIG. 11 above. It is observed that over a period of simulated drillbit revolutions the Beta angles vary significantly, and during asignificant percentage of the time the Beta angles are not at or near180 degrees. The Beta angle plot as a performance parameter is notoptimized and thus the side rake angle distribution that produces such aBeta angle plot is not optimum.

FIG. 28 shows a historic graphical plot of Beta angles between thecircumferential and the radial components of the total imbalance forcessimulated with a drill bit having an improved side rake angledistribution according to one embodiment of the invention, as forexample one of the side rake angle distributions shown in FIGS. 12, 13,14, 15, or in Table 1 above. It is observed that over a period ofsimulated drill bit revolutions the Beta angles are maintained at ornear 180 degrees during a significant period of the simulated drillingtime. The Beta angle plot as a performance parameter may be consideredoptimized and thus the side rake angle distribution that produces such aBeta angle plot may be considered optimized.

The above examples of how graphical displays of several performanceparameters may be used to design drill bits having improved side rakeangle distributions. One of ordinary skill in the art will appreciatefrom the present disclosure that other performance parameters may besimilarly used to improve the side rake angle distributions of a drillbit.

Designing Fixed Cutter Bits

A fixed cutter drill bit designed by the methods of one or more of thevarious embodiments of the invention has been found to have improvedperformance.

In one or more embodiments in accordance with the method shown in FIG.29, bit design parameters are selected at 1152 and may include thenumber of cutters on the bit, cutter spacing, cutter location, cutterorientation, cutter height, cutter shape, cutter profile, cutterdiameter, cutter bevel size, blade profile, bit diameter, etc. andothers of a type that may subsequently be altered by the designengineer. These are only examples of parameters that may be adjusted. Adrill bit having those selected parameters is simulated drilling anearth formation at 1154. At 1153 one or more performance indicatingparameters such as the total imbalance force, the radial components andcircumferential components of the total imbalanced force, the Beta anglebetween the component forces over a period of time, the bottom holepattern, the dynamic trajectory of the centerline of the drill bit,and/or the side rake imbalance forces determined during a simulatedperiod of drilling. Selected design parameters including the side rakeangle distribution may be altered at step 1156 in the design loop 1160.Additionally, bit design parameter adjustments may be entered manuallyby an operator after the completion of each simulation or,alternatively, may be programmed by the system designer to automaticallyoccur within the design loop 1160. For example, one or more selectedparameters may be incrementally increased or decreased within a selectedrange of values for the iteration of the design loop 1160. The methodused for adjusting bit design parameters is a matter of convenience forthe system designer. Therefore, other methods for adjusting parametersmay be employed as determined by the system designer. Thus, theinvention is not limited to a particular method for adjusting designparameters.

In alternative embodiments, the method for designing a fixed cutterdrill bit may include repeating the adjusting of at last one drillingparameter and the repeating of the simulating the bit drilling aspecified number of times or, until terminated by instruction from theuser. In these cases, repeating the “design loop” 1160 (i.e., theadjusting the bit design and the simulating the bit drilling) describedabove can result in a library of stored output information which can beused to analyze the drilling performance of multiple bits designs indrilling earth formations and a desired bit design can be selected fromthe designs simulated.

An optimal set of bit design parameters may be defined as a set of bitdesign parameters which produces a desired degree of improvement indrilling performance, in terms of rate of penetration, cutter wear,optimal axial force distribution between blades, between individualcutters, and/or optimal lateral forces distribution on the bit. Forexample, in one case, a design for a bit may be considered optimizedwhen the resulting lateral force on the bit is substantially zero orless than 1% of the weight on bit.

In one or more other embodiments, the method may be modified to adjustselected drilling parameters and consider their effect on the drillingperformance of a selected bit design, as illustrated in FIG. 29.Similarly, the type of earth formation being drilled may be changed andthe simulating repeated for different types of earth formations toevaluate the performance of the selected bit design in different earthformations. These methods may be used to design and evaluate a bitdesign having optimized side rake distributions for various formationsand/or drilling conditions.

As set forth above, one or more embodiments of the invention can be usedas a design tool to optimize the performance of fixed cutter bitsdrilling earth formations. One or more embodiments of the invention mayalso enable the analysis of drilling characteristics for proposed bitdesigns prior to the manufacturing of bits, thus, minimizing oreliminating the expensive of trial and error designs of bitconfigurations. Further, the invention permits studying the effect ofbit design parameter changes on the drilling characteristics of a bitand can be used to identify bit designs which exhibit desired drillingcharacteristics. Further, use of one or more embodiments of theinvention may lead to more efficient designing of fixed cutter drillbits having enhanced performance characteristics.

Example Alternative Embodiments

FIG. 30 shows a partial end view of a fixed cutter bit 1200 with analternative modification of the distribution of side rake angles alongone exemplary blade 1202 having cutters 1204, 1206, 1208, 1210, and 1212in a cone region 1214 that are positioned with their faces 1216 parallelto a radial plane 1220 through the centerline 1222 of the bit 1200. Bymoving the cutters 1204, 1206, 1208, 1210, and 1212 forward of theradial plane 1220 without tilting the cutters, the faces 1216 continueto be parallel to the radial plane 1220. However the offset distance1218 causes the tangent lines 1224, 1226, 1228, 1230 and 1232 at theface of each cutter 1204, 1206, 1208, 1210, and 1212 to be at adifferent side rake angle 1234, 1236, 1238, 1240 and 1242, respectively,relative to the centerlines of each cutter. Thus, the side rake anglefor each cutter is different and relatively larger at the center cutter1204 and relatively smaller at cutter 1212. This shows an alternativeway to modify the side rake angle distribution. This alternative methodis useful for modifying the side rake angle distribution of drill bitsthat are already designed, by repositioning the cutters forward withinexisting cutter holding sockets and thereby improving performance.

FIG. 31 shows a schematic end view of a dual set fixed cutter drill bit1300 showing a layout of fixed cutters 1-88 both on leading blades 1390,1391, 1392 and 1393 and on trailing blades 1394, 1395, 1396 and 1397 ofa drill bit and showing alternative side rake angle distributions withoutward side rake angles distributed along the cone regions of theleading blades 1390, 1391, 1392 and 1393 and inward side rake anglesdistributed along the cone regions of the trailing blades 1394, 1395,1396 and 1397.

In one or more embodiments, the method described above is embodied in acomputer program and the program also includes subroutines forgenerating a visual displays representative of the performance of thefixed cutter drill bit drilling earth formations.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

1. A method for designing a fixed cutter drill bit, comprising:simulating the fixed cutter drill bit drilling in an earth formation,wherein the fixed cutter drill bit comprises cutters in a cone regionand a nose region having side rake angle; determining at least oneperformance characteristic for the fixed cutter drill bit; adjusting aside rake angle of at least one cutter of the fixed cutter drill bit,wherein the adjusting involves adjusting a cutter along at least one ofthe cone region and the nose region of the fixed cutter drill bit; andrepeating the simulating, the determining, and the adjusting until theat least one performance characteristic meets a selected criterion. 2.The method of claim 1, wherein the adjusting involves a cutter along thecone region of the fixed cutter drill bit.
 3. The method of claim 1,wherein the adjusting involves a cutter along the nose region of thedrill bit.
 4. The method of claim 1, wherein the adjusting produces aside rake angle distribution such that cutters positioned in the coneregion toward a center of the drill bit have larger side rake anglesthan cutters positioned in the nose region of the drill bit.
 5. Themethod of claim 4, wherein the side rake angle distribution is adjustedsuch that cutters in the cone region have progressively smaller siderake angles from the center outward toward the nose region.
 6. Themethod of claim 1, wherein the adjusting produces a side rake angledistribution such that a cutter in the cone region has a side rake angleno greater than about 15 degrees and a cutter in the nose region has aside rake angle smaller than the side rake angle of the cutter in thecone region.
 7. The method of claim 1 wherein determining at least oneperformance characteristic for the simulated fixed cutter drill bitcomprises determining at least one performance characteristic selectedfrom a simulated bottom hole cutting pattern, a simulated totalimbalance force, a simulated side rake imbalance force, a historic Betaangle between radial and circumferential imbalance forces, and ahistoric trajectory of a simulated dynamic centerline.
 8. The method ofclaim 1, wherein simulating further comprises: modeling of the drill bitdynamically drilling in the formation without constraining a centerlineof the drill bit to be coaxial with a centerline of a bore hole.
 9. Themethod of claim 8, wherein modeling of the drill bit dynamicallydrilling in the formation without constraining a centerline of the drillbit to be coaxial with a centerline of a bore hole, further comprisesconstraining the dynamic movement of the centerline of the drill bitbased upon drill string parameters.
 10. The method of claim 1, whereinsimulating further comprises: modeling of the drill bit dynamicallydrilling in the formation while constraining the dynamic movement of thecenterline of the drill bit based upon drill string parameters.
 11. Themethod of claim 1, wherein the cutters in the cone region have faces atan original position and wherein adjusting the side rake angle of atleast a cutter comprises moving the cutter so that the face of thecutter is moved forward in the direction of bit rotation of an imaginaryradial plane, the imaginary radial plane passing through a centerline ofthe drill bit and through an original position of a center of the faceof the cutter.
 12. The method of claim 1, wherein: the simulatingcomprises calculating a wear pattern on a plurality of cutters on thefixed cutter drill bit over the simulated drilling time; and thedetermining comprises entering the calculated wear pattern correspondingto the period of simulated drilling time.
 13. The method of claim 1,further comprising displaying at least one performance parametergraphically, and wherein: the simulating comprises simulating thedrilling in the earth formation for a period of simulated drilling time;the determining comprises determining the at least one performanceparameter for the period of simulated drilling time; and the adjustingthe side rake angle of at least one cutter comprises adjusting a siderake angle distribution of a plurality of cutters along the cone regionof at least one blade of the fixed cutter drill bit to improve the atleast one performance parameter according to the graphically displayedperformance parameter.
 14. The method of claim 13, further comprisingrepeating the simulating, determining, displaying, and adjusting theside rake angle distribution to optimize the performance parameter. 15.The method of claim 13, wherein adjusting the at least the side rakeangle distribution of the cutters along the cone region of the blade ofthe fixed cutter drill bit comprises adjusting the cutters in the conealong a plurality of blades of the fixed cutter drill bit.
 16. Themethod of claim 15, wherein the drill bit comprises a dual set drill bithaving leading blades and trailing blades and wherein adjusting at leastthe side rake angle distribution of the cutters along the cone region ofthe blade of the fixed cutter drill bit comprises adjusting the siderake angles of cutters in the cone region along the leading blades tohave an outward side rake angle and adjusting the side rake angles ofthe cutters in the cone region along the trailing blades to have aninward side rake.
 17. The method of claim 1, wherein the adjustingproduces a side rake angle distribution such that the at least onecutter has a side rake angle greater than 15 degrees and less than 90degrees.
 18. A method for designing a fixed cutter drill bit,comprising: simulating the fixed cutter drill bit drilling in an earthformation; determining at least one performance characteristic for thefixed cutter drill bit; adjusting at least the side rake angledistribution of cutters at least along a cone region of a blade of thefixed cutter drill bit to change the at least one performancecharacteristic of the fixed cutter drill bit.
 19. The method of claim18, further comprising repeating the simulating, determining, andadjusting at least the side rake angle distribution of the cutters tooptimize the performance characteristic.
 20. The method of claim 18,further comprising adjusting at least the side rake angle distributionof the cutters along a nose region of the drill bit.
 21. The method ofclaim 20, wherein adjusting at least the side rake angle distribution ofthe cutters along the cone region and along the nose region of the bladeof the fixed cutter drill bit comprises adjusting the side rake angledistribution such that cutters toward a center of the cone region havelarger side rake angles than cutters toward the nose region of the drillbit.
 22. The method of claim 21, wherein adjusting at least the siderake angle distribution of the cutters along the cone region of theblade of the fixed cutter drill bit comprises adjusting the side rakeangle distribution such that cutters at a center of the cone region haverelatively larger side rake angles than cutters along the nose region ofthe drill bit and such that the side rake angles progressively blendfrom the relatively larger to the relatively smaller side rake angles.23. The method of claim 18, wherein the adjusting produces a side rakeangle distribution such that a cutter in a cone region has a side rakeangle greater than 15 degrees and less than 90 degrees and a cutter in anose region has a side rake angle smaller than the side rake angle ofthe cutter in the cone region.